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SCHOOL    PHYSICS 


A  NEW  TEXT-BOOK 
FOR  HIGH  SCHOOLS  AND  ACADEMIES 


BY 


ELROY   M.   A  VERY,  PH.D.,   LL.D. 
« | 

AUTHOR  OF  A  SERIES  OF  PHYSICAL   SCIENCE  TEXT-BOOKS 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSIOS 


SHELDON   AND   COMPANY 

NEW  YORK  AND   CHICAGO 


*DK.  WERY1 3'  PHYSICAL  SCIENCE  SERIES. 


FIRST   PRINCIPLES  OF   NATURAL   PHILOSOPHY. 
ELEMENTS  OF   NATURAL   PHILOSOPHY. 

SCHOOL    PHYSICS. 

ELEMENTS  OF   CHEMISTRY. 

COMPLETE   CHEMISTRY. 

This  contains  "  The  Elements  of  Chemistry,"  with  an  additional 
chapter  on  Hydrocarbons  in  Series,  or  Organic  Chemistry.  It  can  be 
used  in  the  same  class  with  "  The  Elements  of  Chemistry." 


COPYRIGHT,  1895,  BY 
SHELDON   AND  COMPANY. 


TYPOGRAPHY  BY  J.  8.  GUSHING  &  Co.,  NORWOOD,  MASS. 


PREFACE. 


IN  this  book  will  be  found  an  unusual  number  of  prob- 
lems. It  is  not  intended  that  each  member  of  each  class 
shall  work  all  of  the  problems.  It  is  hoped  that  they -are 
sufficiently  numerous  and  varied  to  enable  you  to  select 
what  you  need  for  your  particular  class.  Xo  author  can 
make  a  comfortable  Procrustean  bedstead. 

For  several  years  there  has  been  a  growing  tendency  in 
the  high  schools  of  the  country  to  indulge  in  laboratory 
methods.  An  effort  has  been  made  to  adapt  this  book  to 
such  needs.  The  author  has  no  sympathy  with  the  idea 
that  the  pupil  should  have  set  before  him  the  impossible 
task  of  rediscovering  all  the  physical  truths  known  to 
modern  science.  Even  were  there  no  other  obstacle,  indi- 
vidual life  is  too  short,  and  but  a  small  part  of  that  short 
period  can  be  given  to  a  high-school  course  in  natural 
philosophy.  Nor  has  he  any  more  sympathy  with  the 
notion  that  the  high-school  laboratory  should  attempt  the 
full  work  of  the  technological  school.  High-school  lab- 
oratory work  has  its  limitations  in  the  capacities  of  the 
pupils,  in  the  time  at  their  disposal,  in  laboratory  equip- 
ment, etc.  Still  it  affords  a  needed  variation  from  the 
old  method  in  which  the  author  stated  facts  ex  cathedra, 

673158 


4  SCHOOL   PHYSICS. 

to  be  accepted  and  memorized  by  the  pupils,  and  from 
the  less  objectionable  plan  in  which  the  teacher  performed 
all  the  experiments  and  the  pupil  simply  observed  and 
admired.  Pedagogic  practice,  having  swung  from  one 
end  of  the  arc  to  the  other,  is  now  settling  down  to  the 
golden  mean.  May  it  prove  that  in  its  excursions  it  held 
fast  to  all  the  good  it  found  and  left  the  rest  behind. 

If,  at  the  beginning  of  an  experiment,  John  Tyndall 
could  ask,  "  For  what  shall  I  look  ?  "  we  may  be  permitted 
to  suggest  that  the  pupil,  ignorant  of  scientific  truths  and 
experimental  methods,  and  without  manipulatory  skill, 
needs  a  text-book  something  like  this  to  save  even  his 
laboratory  practice  from  degenerating  into  chaotic  waste. 
An  effort  has  been  made  by  the  author  of  this  book  to 
introduce  the  pupil  into  what  is  a  new  world  to  him,  to 
give  him  a  few  elementary  lessons  in  the  ways  of  that 
world,  trusting  that,  in  later  years,  other  hands  will  guide 
him  over  more  rugged  paths  and  into  higher  realms. 
But,  no  matter  how  well  an  author's  work  may  have 
been  done,  it  can  never  take  the  place  of  the  living  and 
live  teacher;  it  may  be  a  help,  but  it  certainly  cannot  be 
a  substitute. 

Each  pupil  is  expected  to  perform  as  many  of  the  labo- 
ratory exercises  as  possible.  The  classroom  work  must 
be  kept  ahead  of  the  laboratory  work;  i.e.,  the  pupil 
must  come  to  the  laboratory  with  some  knowledge  of 
the  principles  involved  in  the  work  that  he  is  required  to 
perform.  Even  then,  there  will  be  a  grievous  waste  of 
time  and  effort  unless  the  teacher  is  judicious,  vigilant 
and  firm.  For  instance,  it  will  not  be  easy,  at  the  begin- 
ning, to  lead  pupils  to  appreciate  the  importance  of  mak- 


PREFACE.  5 

ing  all  measurements  as  accurately  as  possible  with  the 
given  instruments,  and  to  realize  that  there  is  value  in 
repeated  measurements  of  the  same  quantity.  Much  of 
the  benefit  to  be  derived  from  laboratory  practice  hangs 
upon  the  cultivation  of  habits  of  accuracy  of  observation, 
the  formation  of  habitually  systematic  methods,  and  the 
development  of  an  ability  to  reason  from  observed  partic- 
ulars to  general  laws.  The  ability  to  generalize  from 
observed  phenomena  should  not  be  expected  of  many,  and 
must  not  be  demanded. 

The  divisions  of  the  class  for  laboratory  practice  should 
be  so  small  that  the  teacher  may  get  to  each  pupil  at  short 
intervals  to  check  gross  errors  at  the  beginning,  and  thus 
prevent  much  waste  of  time.  Ten  or  twelve  is  perhaps  a 
fair  limit  for  the  size  of  such  divisions.  Pupils  should  be 
taught  neatness  and  dexterity  of  manipulation,  held  to  a 
rigid  accountability  for  the  care  and  condition  of  all  appa- 
ratus used  by  them  whether  it  belongs  to  them  or  to  the 
school,  required  to  make  accurate  notes  of  their  work  as 
it  proceeds,  and  encouraged  to' write  them  up  neatly  and 
fully  in  note-books  of  prescribed  form.  They  should  be 
taught  to  put  their  records  into  tabular  form  when  the 
nature  of  the  work  will  permit  such  a  form  of  record. 
Additional  to  all  of  this  is  the  work  of  enforcement; 
questions,  discussions,  supplementary  experiments,  and 
problems.  All  of  this  demands  so  much  of  time  and 
enthusiasm  from  the  teacher,  that  the  school  authorities 
ought  not  to  forget  that  "  to  give  good  instruction  in  the 
sciences  requires  of  the  teacher  more  work  than  to  give 
good  instruction  in  mathematics  and  the  languages,"  and 
that  "  the  teacher  should  be  absolutely  at  liberty,  not  only 


6  SCHOOL  PHYSICS. 

during  the  physics  hours,  but  also  during  several  other 
hours  of  the  week,  to  arrange  for  and  to  direct  the  experi- 
ments, unvexed  by  any  care  of  schoolrooms  or  of  pupils 
save  those  actually  engaged  in  laboratory  work."  If  the 
school  has  not  a  regularly  equipped  physical  laboratory, 
as  is  desirable,  a  room  should  be  set  aside  for  the  exclu- 
sive use  of  classes  in  experimental  physics,  and  fitted  for 
such  use  as  well  as  the  circumstances  of  the  case  will 
allowc 

The  author  has  taken  special  pains  to  select  experiments 
and  exercises  that  may  be  performed  with  simple  and  in- 
expensive apparatus,  and  many  of  them  have  been  devised 
expressly  for  this  work.  The  author  has  not  disdained  any 
aid  that  he  could  draw  from  any  source,  but  he  cheerfully 
acknowledges  his  especial  obligation  to  Professor  Barker's 
"  Physics,"  the  Harvard  College  pamphlet,  and  its  ampli- 
fication in  the  admirable  work  of  Messrs.  Hall  and  Bergen. 
Special  acknowledgments  are  also  due  to  Professor  Dayton 
C.  Miller  of  the  Case  School  of  Applied  Science,  who  has 
read  the  work  in  manuscript  and  in  proof-sheets  ;  to  Mr. 
George  T.  Hanchett  of  Pawtucket,  R.  I.,  for  valuable 
assistance  in  the  chapter  on  Electricity  and  Magnetism; 
and  to  Mr.  Henry  C.  Muckley,  assistant  superintendent  of 
the  public  schools  of  Cleveland,  for  his  many  valuable  sug- 
gestions, and  for  his  aid  in  correcting  proof.  To  the  many 
others  who  have  given  assistance  in  many  ways,  the 
author  tenders  assurances  of  grateful  appreciation. 

The  author  would  be  glad  to  receive  any  suggestions 
from  any  who  may  use  this  book,  or  to  answer  any  inquiries 
concerning  the  study  or  apparatus.  He  may  be  addressed 
at  Cleveland,  O. 


CONTENTS. 


CHAPTER  I. —MATTER. 

PAGE 

I.     DOMAIN  OF  PHYSICS  ;  DIVISIONS  OF  MATTER        ...  9 

II.     PROPERTIES  OF  MATTER         .......  16 

III.     CONDITIONS  OF  MATTER 38 

CHAPTER   II.  —  MECHANICS., 

I.     MOTION  AND  FORCE       ........  57 

II.     WORK  AND  ENERGY 83 

III.  GRAVITATION 95 

IV.  FALLING  BODIES 106 

V.     PENDULUM 118 

VI.     SIMPLE  MACHINES 127 

VII.     MECHANICS  OF  LIQUIDS 150 

VIII.     MECHANICS  OF  GASES 179 

CHAPTER  *  in.  —  ACOUSTICS. 

I.     NATURE  OF  SOUND,  ETC.        .......  201 

II.     VELOCITY,  REFLECTION  AND  REFRACTION    ....  218 

III.  CHARACTERISTICS  OF  TONES  .......  226 

IV.  CO-VIBRATION 244 

V.     LAWS  OF  VIBRATION 258 

7 


g  CONTENTS. 

CHAPTER  IV.  — HEAT. 

PAGE 

I.     NATURE  OF  HEAT,  TEMPERATURE,  ETC 270 

II.     PRODUCTION  AND  TRANSFERENCE  OF  HEAT  ....  276 

III.  EFFECTS  OF  HEAT 283 

IV.  MEASUREMENT  OF  HEAT 299 

V.     RELATION  BETWEEN  HEAT  AND  WORK          ....  306 

CHAPTER   V.— RADIANT   ENERGY. 

I.     NATURE  OF  RADIATION 312 

II.     LIGHT  :  VELOCITY  AND  INTENSITY         .....  314 

III.  REFLECTION  OF  RADIANT  ENERGY         .....  326 

IV.  REFRACTION  OF  RADIANT  ENERGY         .....  347 
V.     SPECTRA,  CHROMATICS,  ETC.          ......  368 

VI.     INTERFERENCE,  DIFFRACTION,  POLARIZATION,  ETC.       .         .  393 

VII.     A  FEW  OPTICAL  INSTRUMENTS 400 

CHAPTER   VI.  —  ELECTRICITY   AND   MAGNETISM. 

I.     GENERAL  VIEW  : 

A.  STATIC  ELECTRICITY  .         .         .         .  ,  .412 

B.  CURRENT  ELECTRICITY       ......  433 

C.  MAGNETISM         .                  .         .         .         .         .         .  454 

II.     ELECTRIC  GENERATORS,  ELECTROMAGNETIC  INDUCTION,  ETC.  478 

III.  ELECTRICAL  MEASUREMENTS 523 

IV.  SOME  APPLICATIONS  OF  ELECTRICITY 543 

V.     ELECTROMAGNETIC  CHARACTER  OF  RADIATION     .         .         .  579 

APPENDIX 591 

INDEX ,597 


CHAPTER  I. 

MATTER. 

I.    DIVISIONS   OF  MATTEK.  — THE   DOMAIN  OF 
PHYSICS. 

• 
"Read  Nature  in  the  language  of  experiment." 

1.  Science  is  classified  knoivledge.     General  information 
is  valuable,  but  it  is  only  when  facts  are  classified  that 
the  knowledge  becomes  scientific  knowledge. 

2.  Matter  is  anything  that  occupies  space  or  '-''takes  up 
room."     Its  existence  is  made  known  to  us  through  the 
senses.     Substances  are  the  different  kinds  of  matter,  as 
water,  wood,  silver,  etc.    A  body  is  any  separate  portion 
of  matter,  as  a  book,  a  table,  or  a  star. 

Structure  of  Matter. 

Experiment  i.  —  Heat  the  mercury  in  the  bulb  of  a  common  ther- 
mometer. The  bulb  remains  full,  but  the  liquid  rises  in  the  tube. 
There  seems  to  be  more  mercury  than  there  was  before.  How  can 
this  be  ?  There  must  be  a  greater  number  of  molecules,  the  molecules 
must  be  larger,  or  they  must  be  further  apart. 

Experiment  2.  —  Make  a  common  goose-quill  pop-gun.  Notice  that 
when  you  use  it  the  air  confined  between  the  two  wads  is  compressed, 
or  made  to  occupy  about  half  its  original  space.  The  air  particles 
were  reduced  in  size  or  in  number,  or  were  crowded  together  more 
closely.  Perhaps  the  matter  of  which  a  body  is  made  does  not  actually  Jill 
all  the  space  which  the  body  seems  to  occupy. 

9 


10  SCHOOL  PHYSICS. 

Experiment  3.  —  Rub  the  smooth  handle  of  a  fine  awl  over  a  piece 
of  fine  wire  gauze,  and  the  gauze  seems  to  present  a  continuous  sur- 
face. Perhaps  it  is  the  fault  of  the  instrument  in  your  hand,  and  not 
the  fault  of  the  gauze.  Rub  the  point  of  the  awl  over  the  gauze,  and 
you  soon  find  openings  between  the  metal  threads.  But  the  openings 
are  there,  whether  you  can  feel  them  or  not. 

Experiment  4. —  Rub  the  point  of  a  fine  sewing  needle  over  the 
surface  of  a  window  pane.  The  glass  seems  to  be  continuous  in  its 
structure,  and  the  needle  cannot  get  through.  Perhaps  it  is  the  fault 
of  the  instrument  you  are  using.  Try  one  more  delicate.  Let  a  ray 
of  light  fall  upon  the  glass,  and  it  easily  finds  a  passageway  between 
the  solid  molecules.  Rays  of  light  are  often  used  by  scientific  men  as 

instruments  for  their  work. 

• 

3.  Structure  of  Matter.  —  Many  facts,  some  of  which 
will  be  considered  later,  indicate  that  matter  is  not  con- 
tinuous  ;  that  any  sensible  portion  of  it  is  a  group  of  very 
small  particles ;    that  no  two  of  these  are  in  actual  con- 
tact;   and  that  the  minute  particles  of   each  group  are 
held  together  by  certain  attractive  forces,  to  which  we 
must  give  careful  consideration  and  earnest  study. 

(a)  When  you  look  at  a  brick  wall  from  a  considerable  distance, 
it  has  an  apparent  uniformity  of  structure.  You  cannot  see  that  it  is 
made  of  many  bricks,  separated  by  mortar-filled  spaces.  This  is  the 
fault  of  your  sense  of  vision.  As  you  come  nearer,  you  see  what  you 
did  not  see  before,  —  the  individual  and  separated  bricks.  But  such 
is  the  structure  of  the  tvall,  ivhether  you  can  see  it  or  not. 

4.  Divisions  of  Matter.  —  Matter  exists  in  atoms,  mole- 
cules, and  masses.     It  is  very  important  that  we  clearly 
understand  what  these  words   mean,  or   we   shall   have 
trouble  in  trying  to  understand  much  that  is  to  follow. 

5.  An  Atom  is  the  smallest  quantity  of  matter  that  can 
enter  into  combination  and  thus  form  molecules  and  masses. 
It  is  the  chemical  unit  of  matter,  and  is  considered  iixdi- 


DIVISIONS   OF  MATTER.  11 

visible.     In  nearly  every  case,  an  atom   is   a   part   of   a 

molecule. 

(a)  We  may  say  that  atoms  are  the  smallest  particles  of  matter 
that  can  exist.  They  seldom  exist  alone,  but  quickly  unite  with 
others  like  themselves  to  form  elementary  molecules,  or  with  others 
unlike  themselves  to  form  compound  molecules.  For  example,  one 
atom  of  oxygen  combines  with  another  like  itself  to  form  an  elemen- 
tary molecule  of  oxygen,  while  one  atom  of  oxygen  combines  with  two 
of  hydrogen  to  form  a  compound  molecule  of  water.  There  are  more 
than  seventy  kinds  of  atoms  now  known. 

6.  A  Molecule  is  a  quantity  of  matter  so  small  that  it 
cannot  be  divided  without  changing  its  nature.     It  is  the 
physical  unit  of  matter,  and  can  be  divided  only  by  a 
chemical   process.      Atoms    make    molecules  ;    molecules 
make  masses. 

(a)  A  molecule  is  so  very  small  that  the  smallest  particle  of  matter 
visible  in  the  best  of  modern  microscopes  contains  millions  of  mole- 
cules. If  a  drop  of  water  could  be  magnified  until  it  appeared  to  be 
as  large  as  the  earth  on  which  we  live,  each  molecule  in  the  drop  thus 
magnified  would  still  look  smaller  than  a  base-ball.  Even  in  dense 
solids,  molecules  are  separated  by  spaces  that  are  large  as  compared  to 
their  own  size.  Tait  assumes  it  as  probable  that  the  molecule  itself 
does  not  occupy  so  much  as  five  per  cent,  of  its  share  of  the  whole 
space.  This  signifies  that  the  distances  between  molecules  is  about 
three  times  the  diameter  of  a  molecule. 

(fe)  Some  compound  molecules  are  very  complex.  The  common 
sugar  molecule  contains  forty-five  atoms  of  three  kinds.  Elementary 
molecules  make  elementary  masses  or  substances.  Compound  mole- 
cules make  compound  masses  or  substances.  The  nature  of  the  mole- 
cule determines  the  nature  of  the  substance. 

(c)  Molecules  are  believed  to  be  in  ceaseless  motion,  but  ever  sub- 
ject to  the  constraining  action  of  certain  molecular  forces.  Many  of 
the  phenomena  observed  in  matter  are  due  to  these  molecular  motions, 
as  will  more  clearly  appear  further  on. 

7.  A  Mass  is  any  quantity  of  matter  that  is  composed  of 
molecules.      Masses   are   elementary  or   compound.      An 


12  SCHOOL  PHYSICS. 

elementary  substance  is  called  an  element.  There  are  as 
many  elements  as  there  are  kinds  of  atoms.  Compound 
substances  are  innumerable. 

(a)  We  may  take  a  lump  of  salt,  which  is  a  mass,  and  break  it  into 
many  pieces ;  each  piece  will  be  a  mass.  We  may  take  one  of  these 
pieces  and  crush  it  to  finest  powder ;  each  grain  will  still  be  a  mass. 
We  may  imagine  one  of  these  grains  of  powdered  salt  to  be  divided 
into  so  many  parts  that  any  further  division  will  change  them  from 
salt  to  something  else ;  these  particles  of  salt,  so  small  that  further 
division  would  change  their  nature,  are  molecules.  If  one  of  these 
molecules  is  divided,  it  ceases  to  be  salt ;  we  have  instead  an  atom  of 
sodium  and  an  atom  of  chlorine. 

(6)  The  quantity  of  matter  constituting  a  mass  is  not  necessarily 
great.  A  drop  of  water  may  contain  a  million  animalcules.  Each 
animalcule  is  a  mass  as  truly  as  the  greatest  monster  of  the  land  or 
sea.  The  dewdrop  and  the  ocean,  clusters  of  grapes  and  clusters  of 
stars,  are  equally  masses  of  matter. 

(c)  The  term  "  mass  "  also  has  reference  to  the  quantity  of  matter 
in  a  body.  This  double  use  of  the  word  is  unfortunate. 

8.  Forms  of  Motion.  —  It  is  probable  that  each  of  these 
three  divisions  of  matter  has  its  own  form  or  mode  of 
motion.  The  motion  of  a  mass  is  often  called  molar  or 
mechanical  motion.  The  motion  of  a  bullet  is  an  example. 
The  motion  of  the  molecules  in  a  mass  constitutes  heat. 
If  a  bullet  strikes  a  target,  the  shock  that  destroys  the 
molar  motion  of  the  bullet  increases  the  vibration  of  the 
molecules  of  which  the  bullet  is  composed.  These  molec- 
ular vibrations  constitute  heat.  When  a  bullet  is  thus 
stopped,  it  is  heated,  and  the  production  of  heat  is  ex- 
plained only  in  this  way.  These  molar  and  molecular 
motions  give  to  matter  the  power  of  doing  work,  the 
scientific  name  of  which  power  is  energy. 

The  motion  of  atoms  within  the  molecule  has  not  been 
proved. 


DIVISIONS  OF  MATTER.  13 

(a)  Fancy  a  million  flies  surrounded  by  an  imaginary  shell.  If 
each  fly  represents  a  molecule,  the  contents  of  the  shell  represent  a 
mass.  Imagine  this  shell  to  be  thrown  through  the  air.  The  motion 
of  the  shell  represents  molar  motion-  As  the  shell  is  moving  through 
the  air,  the  flies  are  moving  slowly  among  themselves  within  the  shell. 
This  motion  of  the  flies  represents  molecular  motion,  and  is  a  very  dif- 
ferent thing  from  the  motion  of  the  shell.  When  the  shell  strikes  the 
ground,  the  molar  motion  is  destroyed,  but  the  molecular  motions 
are  increased,  for  the  flies  are  set  in  much  more  rapid  motion  by  the 
shock.  This  is  just  about  what  happens  when  the  bullet  is  fired 
against  a  target. 

Changes  in  Matter. 

Experiment  5.  —  Hold  a  piece  of  platinum  wire  in  the  flame  of  an 
alcohol  or  of  a  Bunsen  lamp.  It  becomes  hot,  glows,  emits  light. 
There  has  been  a  change  in  the  platinum.  Remove  the  wire  and 
allow  it  to  cool.  Can  you  see  that  the  wire  was  permanently  changed 
in  any  way  by  the  experiment  ? 

Experiment  6.  —  AVith  forceps,  hold  a  piece  of  magnesium  wire  in 
the  flame  of  an  alcohol  or  of  a  Bunsen  lamp.  It  becomes  hot,  glows, 
emits  light.  At  the  end  of  the  experiment  do  you  notice  any  perma- 
nent change  in  the  magnesium  wire? 

9.  Physical  and  Chemical  Changes.  —  Any  change  that 
alters  the  constitution  of  the  molecule,  and  thus  affects 
the    identity   of    the    substance,    is    a    chemical    change. 
Other  changes  in  matter  are  physical  changes. 

10.  Phenomena,  etc.  —  Any  directly  observed  change  in 
matter  is   a  phenomenon.      A   supposition    (or   scientific 
guess)    advanced    in    explanation    of    phenomena   is    an 
hypothesis.     The  value  of  an  hypothesis  increases  with 
the  variety  of  the  phenomena  for  which  it  can  offer  an 
exclusive   explanation.      As   this   variety   increases,   the 
hypothesis  rises  to  the  rank  of  a  theory.    When  the  theory 
has  acquired  so  high  a  degree  of  probability  that  it  is 


14  SCHOOL  PHYSICS. 

accepted  by  the  judicious  as  an  established  truth,  i.e., 
when  it  is  easier  for  men  to  believe  it  than  to  doubt  it, 
it  becomes  a  law,  e.g.,  the  law  of  gravitation.  In  the 
words  of  Mr.  Huxley,  "  Law  means  a  rule  which  we  have 
always  found  to  hold  good,  and  which  we  expect  always 
will  hold  good." 

Force. 

Experiment  7.  —  Mount  each  of  two  4x8  inch  boards  on  the  trucks 
of  a  pair  of  roller  skates  (preferably  with  ball  or  roller  bearings), 
adjusting  the  parts  so  that  the  two  carriages  will  run  in  straight  lines 
when  set  in  motion  on  a  level  surface.  See  that  the  bearings  are  well 
oiled.  Provide  two  smooth,  straight  boards,  6  ft.  x  6  in.  Cut  two 
wooden  blocks  with  thickness  equal  to  the  elevation  of  the  body  of  the 
carriage;  i.e.,  so  that  they  may  just  Slip  under  the  mounted  boards 
when  the  carriages  rest  on  smooth  surfaces.  Nail  one  of  these  blocks 
across  the  face  of  each  of  the  smooth  boards  at  its  end.  Raise  the 


«MG.    1. 

other  end  of  one  of  the  boards  a  little,  until  by  trial  you  find  that 
one  of  the  carriages  will  roll  down  the  incline  with  a  velocity  as 
nearly  uniform  as  is  attainable,  thus  eliminating  largely  the  resist- 
ance due  to  friction.  Fasten  the  board  in  this  position.  Similarly 
adjust  the  other  board  to  the  other  carriage,  and  place  it  side  by  side 
with  the  first  board.  If  the  second  carriage  runs  less  freely  than  the 
first,  the  second  board  will  require  a  greater  incline  than  the  first 
board.  Provide  two  pieces  of  elastic  tape  or  of  black-rubber  tubing, 
each  |  of  a  yard  long.  Stitch  or  clarnp  together  one  end  of  each. 
Stretch  the  joined  pieces,  and  fasten  their  free  ends  at  points  3  yards 
apart.  Tf  the  pieces  stretch  unequally,  trim  the  edges  of  the  stiffer 
piece  until  the  seam  that  joins  the  two  pieces  shall  be  midway  between 
the  fixed  ends.  Loosen  the  fastenings  at  the  ends  of  the  tape,  and  rip 
the  seam  at  the  middle ;  the  tensions  of  the  two  pieces,  when  equally 


DIVISIONS   OF   MATTER.  15 

stretched,  will  pull  with  equal  forces.  Tack  bne  end  of  each  elastic  to 
the  top  of  one  of  the  blocks  at  the  lower  end  of  the  smooth  board,  and 
the  other  end  of  the  elastic  to  the  under  side  of  the  board  that  consti- 
tutes the  body  of  the  carriage  that  was  adjusted  for  that  board ;  the 
elastic,  when  stretched,  will  be  parallel  to  the  long  board.  Similarly 
fasten  the  other  elastic  to  the  other  block  and  carriage.  Load  one 
carriage  with  a  chalk  box  filled  with  iron  nails,  scraps  of  lead,  or  other 
heavy  material ;  load  the  other  with  a  box  of  chalk.  Draw  the  car- 
riages toward  the  upper  ends  of  their  respective  boards  so  as  to  stretch 
the  elastics  considerably  and  equally  ;  release  them  at  the  same  time, 
and  notice  the  speeds  at  which  they  are  drawn  by  the  equal  forces. 
Try  to  find  some  relation  between  the  two  velocities  and  the  weights 
of  the  two  loaded  carriages.  Transfer  part  of  one  load  to  the  other 
carriage  until  they  will  be  moved  with  equal  velocities,  and  determine 
the  approximate  relation  between  the  weights  of  the  two  loaded 
carriages. 

11.  Force.  —  Every  phenomenon  necessarily  implies  a 
change ;  every  change  necessarily  implies  a  cause.  The 
causes  that  produce  phenomena,  or  changes  in  matter,  are 
called  forces.  The  word  "  force  "  is  difficult  of  satisfactory 
definition.  As  generally  used  in  physical  discussions, 
force  signifies  the  immediate  cause  that  produces,  or  tends  to 
produce,  a  change  in  the  velocity  or  direction  of  motion  of  a 
body  ;  i.e.,  a  push  or  a  pull.  Pushes  are  often  called  pres- 
sures ;  and  pulls,  tensions.  Forces  act  on  matter.  Equal 
forces  produce  equal  velocities  when  applied  for  the  same 
length  of  time  to  equal  masses.  Matter  may  now  be 
defined  as  that  which  can  exert  force  or  be  acted  on  by  a 
force. 

(a)  If  the  intensity  of  a  force  varies  in  successive  intervals  of  time, 
it  is  said  to  be  variable  ;  if  its  intensity  does  not  change,  it  is  said  to 
be  constant.  Forces  acting  between  masses  of  matter  separated  by 
sensible  distances  are  called  molar  forces;  e.g.,  gravitation.  Forces 
acting  between  molecules  separated  by  insensible  distances  are  called 
molecular  forces ;  e.g.,  cohesion.  Forces  acting  between  the  atoms  of 
molecules  are  called  atomic  forces ;  e.g.,  chemism. 


16  SCHOOL  PHYSICS. 

12.  Experiments.  —  A  physical  experiment  is  the  produc- 
tion of  physical  phenomena  under  conditions  that  are  con- 
trolled by  a  scientific  student.     It  is  a  question  addressed 
to  Nature  in  the  only  language  that  she  understands. 
The  value  attached  to  her  replies  involves  a  firm  belief 
in  the  " constancy  of  nature;"  i.e.,  that  under  the  same 
physical  conditions  the  same  physical  results  will  always 
be  produced.     Its  purpose  is  to  discover  or  to  illustrate 
some  physical  truth. 

(a)  If  the  experiment  simply  shows  how  something  acts,  it  is 
qualitative ;  if  it  shows  how  much  something  acts,  it  is  quantitative. 

13.  Physics  is  the  branch  of  science  that  treats  of  the  laws 
and  physical  properties  of  matter  and  of  those  phenomena  that 
depend  upon  physical  changes.     It  is  essentially  an  experi- 
mental science.    With  the  explanation  that  energy  signifies 
the  power  of  doing  work,  physics,  in  its  most  general  sense, 
may  be  defined  as  the  science  that  treats  of  matter  and 
energy. 

II.    THE   PROPERTIES   OF   MATTER. 

14.  Properties  of  Matter.  —  Any  quality  that  belongs  to 
matter,  or  is  characteristic  of  it,  is  called  a  property  of  mat- 
ter.    Any  property  that  can  be  shown  without  a  chemical 
change  is  a  physical  property. 

15.  Extension  is  that  property  of  matter  by  virtue  of 
which  it  occupies  space.     It  has  reference  to  the  qualities 
of  length,  breadth,  and  thickness.    It  is  an  essential  prop- 
erty of  matter,  involved  in  its  very  definition. 

(a)  All  matter  must  have  these  three  dimensions.  We  say  that  a 
line  has  length,  a  surface  has  length  and  breadth ;  but  lines  and  sur- 
faces are  mere  conceptions  of  the  mind,  and  have  no  material  exist 


THE  PROPERTIES  OF  MATTER.  17 

ence.     The  third  dimension,  which  affords  the  idea  of  solidity  or 
volume,  is  necessary  to  every  form  of  every  kind  of  matter. 

16.  Measurement  of  Extension.  —  There  are  two  linear 
units  in  use  in  this  country,  —  the  English  yard  and  the 
international  meter.      From  these  are  derived  units   of 
area  and  of  volume. 

17.  The  Yard  is  the  distance  between  two  certain  marks 
on  gold  plugs  set  in  a  certain  bronze  bar,  when  the  bar  is 
at  a  temperature  of  62°  F.     This  bar  is  kept  in  the  Tower 
of  London. 

(a)  The  divisions  of  the  yard,  as  feet  and  inches,  together  with  its 
multiples,  as  rods  and  miles,  are  in  familiar  use.  The  units  of  sur- 
face are  squares  whose  sides  are  some  one  of  the  units  of  length,  as 
the  square  yard  or  the  square  mile.  The  units  of  volume  are  cubes 
whose  edges  are  some  one  of  the  units  of  length,  as  the  cubic  yard 
or  the  cubic  inch. 

(6)  The  standard  gallon  contains  231  cubic  inches. 

18.  The  Meter.  —  The  international  meter  is  the  dis- 
tance between  two  certain  lines  on  a  certain  platiniridium 
bar,  when  the  bar  is  at  the  temperature  of  0°  C.     It  is 
equal,  as  nearly  as  can  be  ascertained,  to  39.37  inches,  or 
"three  feet,  three  inches  and  three  eighths."     This  bar  is 
kept  at  Sevres,  near  Paris.     Like  the  Arabic  system  of 
notation  and  the  table  of  United  States  money,  the  divi- 
sions and  multiples  of  the  meter  vary  in  a  tenfold  ratio, 
hence  some  of  the  great  advantages  of  the  system  based 
upon  it.     This  system  is  in  familiar  use  by  the  people 
of  most  of  the  civilized  countries  of  the  world  and  by 
scientists  of  all  nations.     The  scientific  unit  of  length  is 
the  centimeter,  —  the  one-hundredth  part  of  the  meter. 

(a)  The  United  States  government  very  carefully  preserves,  at  the 
office  of  standard  weights  and  measures  in  Washington,  three  accu- 
rate copies  of  the  international  meter.  These  are  authorized  by 


18 


SCHOOL  PHYSICS. 


congress  as  the  standards  of  length  for  this  country.     The  length  of 
the  yard  is  determined  by  the  relation  above  stated. 


.001  m.  =      0.03937  inch. 
.01    m.  =      0.3937       " 
.1      m.  =      3.937      inches. 

m.  =    39.37 

m.  =  393.7  " 

m.  =  328  feet  1  inch. 

m.  =      0.62137  mile. 

m.  =      6.2137    miles. 


19.    Metric  Measures  of  Length.     Ratio  =  i :  10. 

f  Millimeter      (mm.)  = 
DIVISIONS.      \  Centimeter      (cm.)    = 
{  Decimeter      (dm.)  = 
UNIT.  Meter  (m.)     =          1. 

Dekameter     (D?n.)  =        10. 
MULTIPLES.      Hekt°meter  (Hm.)  =      100. 
Kilometer       (Km.)  =    1000. 
Myriameter  (Mm.)  =  10000. 

The  table  may  be  read,  "  10  millimeters  make 
1  centimeter,  10  centimeters  make  1  decimeter," 
etc.  The  denominations  most  used  in  practice  are 
printed  in  Italics.  The  system  of  nomenclature  is 
very  simple.  The  Latin  prefixes  milli-,  centi-,  and 
deci-j  signifying  respectively  .001,  .01,  and  .1,  and 
'  already  familiar  in  the  mill,  cent,  and  dime  of 
United  States  money,  are  used  for  the  divisions ; 
while  the  Greek  prefixes  deka-,  hekto-,  kilo-,  and 
myria-,  signifying  respectively  10,  100,  1,000,  and 
10,000,  are  used  for  the  multiples  of  the  unit. 
„•  Each  name  is  accented  on  the  first  syllable. 

«  20.  Metric  Measures  of  Surface  and  of 
5  Volume.  —  As  with  English  measures,  the 
metric  units  of  surface  and  volume  are 
surfaces  or  cubes  whose  sides  or  edges 
respectively  are  some  one  of  the  units  of 
length,  as  the  square  meter  or  the  cubic 
centimeter.  For  square  measures,  the  ra- 
tio is  1 : 102  =  1 : 100  ;  thus,  one  hundred 
square  millimeters  make  one  square  centi- 
meter, etc.  For  cubic  measures,  the  ratio 
is  1  :  103  =  1  :  1000  ;  thus,  one  thousand 
cubic  centimeters  make  one  cubic  deci- 
FIQ.  2.  meter,  etc. 


THE   PROPERTIES   OF   MATTER.  19 

21.    Metric  Measures  of  Capacity.     Ratio  =  i :  10.  —  For 

many  purposes,  such  as  the  measurement  of  articles  usually 
sold  by  dry  or  liquid  measure,  a  smaller  unit  than  the 
cubic  meter  is  desirable.  For  such  purposes,  the  cubic 
decimeter  has  been  selected  -as  the  standard,  and  when  thus 
used  is  called  a  liter  (pronounced  leeter). 

In  value  it  is  intermediate  between  the  liquid  and  the 
dry  quarts. 

CMilliliter  (ml.)  =  1  cu.  cm.  =  0.061022  cu.  in. 

DIVISIONS,      -j  Centiliter  (d.)    =  10       "        =  0.338  fluid  oz. 

[  Deciliter  (««.)   =  100       "        =  0.845  gill. 

UNIT.                 Liter  (f.)     =  1000       "        =  1.0567  liquid  qta. 

f  Dekaliter  (Z>/.)  =  10  cu.  dm.  =  9.08  dry  qts. 

MULTIPLES.    \  Hektoliter  (HI.)  =  100       "        =2  bu.  3.35  pks. 

[  Kiloliter  (JO.)  =  1  cu.  m.    =  264.17  gals. 

LABORATORY  EXERCISES. 

Apparatus,  etc.,  Needed.  —  A  notebook  made  of  good  paper,  and 
having  some  of  its  pages  ruled  in  little  squares ;  paper;  pencil ;  a  school 
rule ;  a  yardstick  graduated  to  eighths  of  an  inch ;  a  meter  stick  grad- 
uated to  millimeters ;  a  quart  measure ;  a  liter  measure ;  a  glass  vessel 
graduated  to  cubic  centimeters,  i.e.,  a  graduate  (see  Fig.  3). 

1.  With  a  yardstick,  measure  the  length  of  your  laboratory. 

2.  From  the  table  given  in  §  19,  compute  the  equivalent  of  that 
length  in  meters  and  decimals  thereof. 

3.  With  a  meter  stick,  measure  the  length  of  your  laboratory,  and 
compare  the  result  with  that  obtained  by  computation. 

4.  With  a  meter  stick,  measure  the  door  of  your  laboratory,  and 
make  an  outline  sketch  thereof,  using  the  scale  of  1 : 20. 

5.  With  a  yardstick,  measure  the  width  of  your  laboratory.     Draw 
a  ground  plan  of  the  room,  using  the  scale  of  one  inch  to  the  yard. 

6.  Make  the  necessary  measurements  and  compute  the  capacity 
of  the  room  (a)  in  cubic  feet,   (b)  in  cubic  meters,   (c)  in  gallons, 
(d)  in  liters. 

7.  With  the  meter  stick,  measure  the  length  of  this  leaf  of  your 
book.     Place  the  stick  on  its  edge  so  as  to  bring  the  graduation  as 
close  as  possible  to  the  object  to  be  measured.     Bring,  not  the  end  of  / 


20  SCHOOL  PHYSICS. 

the  rod,  but  one  of  the  centimeter  marks,  even  with  one  end  of  the 
leaf,  and  from  the  stick  read  the  length  of  the  page  accurately  to 
0.1  mm.  You  can  divide  the  smallest  division  on  the  scale  into  tenths 
by  the  eye. 

8.  As  an  exercise  in  subdividing   distances  by  the  eye,  let  the 
teacher  draw  a  tine  line,  curved  or  straight,  on  cross-section  paper, 
designate  certain  lines  as  axes  of  coordinates,  and  require  each  pupil 
in  succession  to  record  in  tabular  form  the  locus  of  each  point  where 
the  given  line  crosses  one  of  the  lines  ruled  on  the  paper. 

9.  Make  two  fine  marks  with  a  sharp  knife  on  a  table-top  or  other 
board,  as  far  apart  as  is  convenient,  the  distance  being  more  than  a 
meter.     Measure  as  accurately  as  possible  the  distance  between  the 
marks,  estimating  fractions  of  millimeters  to  tenths,  and  expressing 
the  results  in  meters.     Do  this  ten  times.     Measure  the  same  distance 
in  inches,  estimating  fractions  of  the  smallest  division  on  the  scale  to 
tenths.     Express  these  results  in  inches  and  decimals  of  an  inch.     Do 
this  ten  times.     Divide  the  average  number  of  inches  by  the  average 
number  of  meters ;  the  quotient  will  be  the  number  of  inches  in  a 
meter.     Express  in  millimeters  the  measures  that  you  took  in  meters, 

and  divide  the  average  number  of  millimeters  by  the 
average  number  of  inches;  the  quotient  will  be  the 
number  of  millimeters  in  an  inch.  Compare  your  re- 
sults with  the  table  given  in  §  19. 

10.  With  the  graduate,  measure  250  cu.  crn.  of  water, 
and  pour  it  into  the  liter  measure.  See  how  often  you 
can  repeat  the  work  without  overflowing  the  measure. 
It  will  require  careful  attention  to  tell  just  when  the 
water  level  reaches  the  required  mark.  The  liquid 
climbs  up  the  sides  of  the  glass,  so  that  it  is  difficult 
to  tell  where  the  water-level  really  is.  The  eye  of  the 
observer  should  be  placed  on  the  level  of  the  required 
mark  011  the  graduate. 
11.  Compute  the  number  of  cubic  centimeters  in  a  quart.  Test 
your  result  by  the  actual  measurement  of  water  or  of  dry  sand. 

Impenetrability. 

Experiment  8.  —  Pass  a  funnel  (or  a  funnel-tube)  and  a  bent 
tube,  as  shown  in  Fig.  4,  through  the  cork  of  a  bottle.  Be  sure  that 
all  joints  are  air-tight.  The  delivery-tube  is  best  made  of  glass,  which 


THE  PROPERTIES  OF  MATTER.  21 

may  be  bent  when  heated  to  redness  in  an  alcohol  or  gas  flame. 

Place  the  end  of  the  delivery-tube  in   a  tumbler  of  water.      Pour 

water  through  the  funnel.     As  it  runs  into 

the  bottle,  air  will  be  forced  out,  and  may 

be  seen  bubbling  through  the  water  in  the 

tumbler.      Directions  for  glass  working  may 

be  found  in  Avery's  Chemistry,  Appendix  4. 

Experiment  9.  —  Thrust  a  lamp  chimney 
into  water.  The  water  will  rise  inside  the 
chimney,  entering  at  the  lower  end,  and, 
pushing  the  air  out  at  the  top.  Repeat  the 
experiment,  closing  the  upper  end  of  the  FIG. 

chimney  with  the  hand   (or  use  an  inverted 

tumbler).     The  water  cannot  rise  as  before,  because  the  vessel  is  filled 
with  air  that  cannot  escape. 

22.  Impenetrability  is  that  property  of  matter  by  virtue 
of  which  two  bodies  cannot  occupy  the  same   space   at  the 
same  time. 

(a)  Illustrations  of  this  property  are  very  simple  and  abundant. 
Thrust  a  finger  into  a  tumbler  of  water ;  it  is  evident  that  the  water 
and  the  finger  are  not  in  the  same  place  at  the  same  time.  Drive  a 
nail  into  a  piece  of  wood;  the  particles  of  wood  are  either  crowded 
more  closely  together  to  give  room  for  the  nail,  or  some  of  them  are 
driven  out  before  it.  Clearly,  the  iron  and  the  wood  are  not  in  the 
same  place  at  the  same  time.  The  familiar  method  of  measuring  the 
volume  of  an  irregular  solid  by  immersing  it  in  a  liquid  and  then 
measuring  the  volume  of  the  liquid  displaced  by  it,  implies  the  impen- 
etrability of  matter. 

23.  Mass   and  Weight. — The  mass  of   a  body  is   its 
quantity  of  matter.      The  weight  of  a  body  is,  in  general 
terms,  the  measure  of  the  earth's   attraction  for  it.      The 
weight  of  a  body  varies  as  its  mass,  and  with  the  posi- 
tion of   the  body  relative  to  the  earth's  surface.     The 
mass  of   a  given  body  is  constant ;    its  weight   is  not. 
The  word  "  mass  "  signifies  matter  ;  the  word  "  weight " 
signifies  force. 


22  SCHOOL  PHYSICS. 

(a)  If  the  given  body  could  be  carried  to  the  moon,  its  weight  there 
would  be  the  measure  of  the  attraction  existing  between  the  body  arid 
the  moon ;  but  as  the  mass  of  the  moon  is  less  than  that  of  the  earth, 
the  attraction  between  the  body  and  the  moou  would  be  less  than 
that  between  that  body  and  the  earth.  The  mass  of  the  given  body 
would  be  the  same  as  it  was  on  the  earth,  but  its  weight  would 
be  less. 

24.  Measurement  of  Mass  and  Weight.  —  Unfortunately 
we  still  have  two  systems  of  measurement, — one  practically 
limited  in  use  to  the  United  States  and  the  British  Em- 
pire ;  the  other,  international.  The  English  unit  of  mass 
is  the  quantity  of  matter  contained  in  the  avoirdupois 
pound.  The  international  unit  of  mass  is  the  kilogram, 
a  certain  piece  of  platiniridium  deposited  at  Sevres,  near 
Paris.  For  many  scientific  uses,  this  unit  is  too  large ; 
and  the  gram,  which  is  the  one-thousandth  part  of  the 
kilogram,  is  generally  used. 

(a)  The  mass  of  a  gram  was  intended  to  be,  and  is  very  nearly, 
equal  to  the  quantity  of  matter  in  one  cubic  centimeter  of  distilled 

water  at  the  temperature 
of  4°  C.  As  with  the 
meter,  the  United  States 

_WEIGHS      e.:|H9il,mL     government  carefully  pre- 
serves   a    standard  kilo- 


gram. 

(6)  The  units  of  weight 

measure    the   attractions 

of   the   earth    for    these 
FIG.  5.  units  of  mass,  and  receive 

the  same  names.     Under 

like  conditions,  a  comparison  of  weights  may  be  substituted  for  a  com- 
parison of  masses,  since  at  any  one  place  the  weight  varies  as  the 
mass.  Unfortunately  we  have  in  common  use  pounds  Troy,  avoir- 
dupois, and  apothecaries',  the  use  varying  with  the  nature  of  the 
transaction.  On  the  other  hand,  the  kilogram  is  definite,  having  but 
a  single  value. 


THE  PROPERTIES   OF   MATTER. 


23 


25.    Metric  Measures  of  Weight. 

[  Milligram  (?ng.)  = 
j  Centigram  (eg.)  = 
v.  Decigram 

Gram 

f  Dekagram 
I  Hektogram    (Hg.)  = 
]  Kilogram        (Kg-)   — 
I  Myriagram 

(a)  A  five-cent  nickel  coin  weighs  five  grams, 
of  water  weighs  one  gram. 


DIVISIONS. 
UNITS. 


MULTIPLES. 


Ratio=i:  10. 

0.0154  grain. 
0.1543      « 
1.5432  grains. 
15.432 

0.3527  oz.  avoirdupois. 
3.5274  « 
2.2046  Ibs. 
(Mg.}  =  22.046      « 

A  cubic  centimeter 


CLASSROOM   EXERCISES. 

1.  How  much  water  by  weight  will  a  liter  flask  contain? 

2.  If  sulphuric  acid  is  1.8  times  as  heavy  as  water,  what  weight  of 
the  acid  will  a  liter  flask  contain  ? 

3.  If  alcohol  is  0.8  times  as  heavy  as  water,  how  much  will  1,250 
cu.  cm.  of  alcohol  weigh  ? 

4.  What  part  of  a  liter  of  water  is  250  g.  of  water? 

5.  What  is  the  weight  of  a  cubic  decimeter  of  water? 

6.  What  is  the  weight  of  a  deciliter  of  water? 

7.  How  many  gallons  of  water  may  be  held  by  a  vessel  18  x  19  x  20 
inches  in  dimensions  ? 

8.  How7  many  liters  of  water  may  be  held  by  a  vessel  measuring 
25  x  35  x  75  cm.? 

LABORATORY  EXERCISES. 

-Additional  Apparatus, 
etc.  —  A  fairly  delicate 
balance  (see  Fig.  6) ; 
English  and  metric 
weights ;  two  rectan- 
gular wooden  blocks, 
2x3x4  inches ;  an 
iron  ball  an  inch  or  two 
in  diameter ;  a  base- 
ball ;  a  croquet  ball ;  a 
pair  of  compasses  with 
pencil  point ;  a  pen- 
knife;  a  teacupful  of 
lead  bullets;  a  bottle; 
wire. 

1.  Measure  the  mass  FlG-  6- 

of  each  of  the  three  balls  in  English  weight  units. 


24  SCHOOL  PHYSICS. 

2.  Compute  the  metric  equivalents  of  these  three  weights. 

3.  Weigh  the  three  balls,  using  metric  standards,  and  compare 
results  with  those  found  by  computation. 

4.  Place  a  meter  stick  on  the  table,  and  by  its  edge  place  two  rectan- 
gular blocks  (chalk  boxes  will  answer  for  rough  work).     Place  a  cro- 
quet ball  between  the  blocks.     Move  the  blocks  as  near  each  other  as 
possible  with  the  ball  between  them,  keeping  one  face  of  each  block 
in  contact  with  the  straight  edge  of  the  meter  stick,     (a)  What  is  the 
diameter  of  the  ball?     (6)  What  is  the^area  of  its  surface? 

5.  (a)   In  similar  manner,  measure  the  diameter  of  a  base-ball, 
(ft)  On  paper,  draw  a  circle  of  that  diameter,     (c)  Compute  the  area 
of  that  circle,     (rf)  With  a  sharp  penknife,  cut  out  the  circle,  and 
pass  the  base-ball  through  the  hole. 

6.  (a)  In  similar  manner,  measure  the  diameter  of  the  iron  ball. 
(&)  Compute  its  volume,     (c)  Compute  the  weight  of  the  same  volume 
of  water,     (d)  Measure  out  and  weigh  that  volume  of  water,  and  com- 
pare its  weight  with  the  computed  result,     (e)  Iron  is  how  many 
times  as  heavy  as  water?     (y)  Place  the  iron  ball  in  a  tumbler  or 
beaker  filled  with  water ;  catch  and  measure  the  water  that  runs  over. 
(</)  How  does  this  measure  compare  with  the  computed  volume  of 
the  ball? 

CAUTION.  —  The  pupil  must  clearly  understand  that  all  measure- 
ments made  by  him  in  this  course  are  extremely  rude,  and  scarcely 
comparable  with  the  measurements  of  precision  made  by  scientists. 
Measurements  to  the  hundred-thousandth  of  an  inch  and  the  twenty- 
thousandth  of  a  second  are  frequently  made,  and  no  painstaking  is 
deemed  too  great  if  it  will  increase  the  degree  of  accuracy  attained. 

7.  From  a  coil  of  moderately  fine  wire  (say,  No.  30)  of  unknown 
length,  cut  off  a  piece  exactly  a  meter  long,  and  weigh  it  carefully. 
Weigh  the  rest  of  the  coil,  and  from  the  two  weights  compute  the 
length  of  the  wire.     Verify  your  result  by  actual  measurement.     If 
the  error  of  your  result  exceeds  1  per  cent.,  repeat  the  work. 

8.  Weigh  a  dry,  clean  bottle.     Fill  the  bottle  with  cold  water,  wipe 
its  outside  surface  dry,  and  weigh  the  filled  bottle  in  metric  units. 
From  the  weight  of  the  water,  determine  the  capacity  of  the  bottle. 
Test  the  result  by  measurement  with  the  graduate. 

9.  Weigh  each  of  five  bullets   at  least   three  times.     For  each 
bullet  take  the  average  of  the  several  weighings  as  the  true  weight. 
Combine  these  several  averages  to  find  the  weight  of  the  average 
bullet.     Count  the  bullets  on  hand.     Multiply  the  weight  of  the  aver- 


THE  PROPERTIES   OF  MATTER. 


25 


age  bullet  by  the  number  of  bullets,  and  compare  the  result  with  the 
mass  of  all  the  bullets  as  determined  by  weighing  them  together. 

Indestructibility. 

Experiment  10.  —  Into  a  glass  tube  2  cm.  in  diameter,  and  15  or 
20  cm.  in  length,  having  one  end  closed  and  rounded  like  a  test-tube, 
place  20  mg.  of  freshly  burnt  charcoal.  Draw  the  upper  part  of  the 
tube  out  to  a  narrow  neck.  Fill  the  tube  with  dry  oxygen,  and  seal 
the  tube  by  fusing  the  neck.  Weigh  the  tube  and  its  contents  very 
carefully.  By  gradually  heating  the  rounded  end  of  the  tube,  the 
charcoal  may  be  ignited,  and,  with 
sufficient  care,  entirely  burned  without 
breaking  the  tube.  When  the  char- 
coal has  disappeared,  weigh  the  tube 
and  its  contents  again.  The  chemical 
changes  that  led  to  the  disappearance  of 
the  charcoal  have  caused  no  change  in 
the  weight  of  the  materials  used. 


FIG.  7. 


26.     Indestructibility    is    that 
property  of  matter  by  virtue  of 
which    it    cannot    be    destroyed. 
The  science  of  chemistry  is  based  on  this  fact,  the  "  con- 
servation of  matter." 

Inertia. 

Experiment  n.  —  Upon  the  tip  of  the  forefinger  of  the  left  hand 
place  a  common  calling  card.     Upon  this  card,  and  directly  over  the 

finger,  place  a  cent.  With  the  nail 
of  the  middle  finger  of  the  right 
hand  let  a  sudden  blow  or  "snap" 
be  given  to  the  card.  A  few  trials 
will  enable  you  to  perform  the 
experiment  so  as  to  drive  the  card 
away,  and  leave  the  coin  resting  upon 
the  finger.  Repeat  the  experiment 
with  the  variation  of  a  bullet  for 
the  cent  and  the  open  top  of  a  bot- 
tle for  the  finger  tip. 


FIG.  8. 


26  SCHOOL  PHYSICS: 

Experiment  12.  —  Suspend  a  heavy  weight  by  a  string  not  much 
stronger  than  is  necessary  to  carry  the  load.  Attach  a  similar  string 
to  the  under  side  of  the  weight.  Pull  steadily  downward  on  the  lower 
string;  in  a  majority  of  cases  the  upper  string  will  break,  for  it  has 
to  support  the  weight  and  resist  the  pull,  while  the  lower  string  has 
only  to  resist  the  pull. 

Support  the  weight  as  before.  Pull  suddenly  downward  on  the 
lower  string :  in  a  majority  of  cases  the  lower  string  will  break,  as  if 
there  was  not  time  enough  for  the  pull  to  pass  through  the  weight  and  reach 
the  upper  string. 

Experiment  13.  —  Suspend  an  iron  ball  weighing  at  least  10  pounds 
by  a  long,  stout  string  from  a  firm  support.  Safety-valve  weights 
may  be  bought  for  a  few  cents  a  pound,  and  answer  admirably  for 
many  such  purposes.  Tie  a  string  strong  enough  to  carry  a  weight  of 
several  pounds  to  the  ball,  and  with  sudden  motion  pull  the  ball 
horizontally.  If  the  pull  is  sudden  enough,  the  string  will  break  with- 
out giving  much  motion  to  the  ball.  This  "hanging  back"  of  the 
ball  is  very  important,  and  must  at  least  be  given  a  name.  Replace 
the  stout  string  by  a  thread,  and  by  a  series  of  gentle,  well-timed 
pulls,  set  the  ball  swinging.  When  it  is  in  rapid  motion,  try  to  stop 
that  motion  by  a  single  pull  on  the  thread.  It  will  be  seen  that  the 
ball  can  go  ahead  as  well  as  hang  back. 

27.  Inertia  signifies  the  tendency  of  matter  at  rest  to 
remain  at  rest,  and  of  matter  in  motion  to  move  with  uni- 
form velocity  in  a  straight  line. 

(a)  Illustrations  of  the  inertia  of  matter  are  so  numerous,  that  there 
should  be  no  difficulty  in  getting  a  clear  idea  of  this  property.  The 
"  running  jump "  and  "  dodging "  of  the  playground,  the  frequent 
falls  which  result  from  jumping  from  cars  in  motion,  the  backward 
motion  of  the  passengers  when  a  car  is  suddenly  started  and  their  for- 
ward motion  when  the  car  is  suddenly  stopped,  the  difficulty  in  start- 
ing a  wagon  and  the  comparative  ease  of  keeping  it  in  motion, 
illustrate  inertia.  By  virtue  of  inertia,  a  cannon  ball  pierces  the 
hardened  steel  armor  of  a  battle  ship ;  and  because  of  the  same  prop- 
erty, it  is  well  not  to  kick  the  cannon  ball,  even  when  it  is  resting  on 
a  smooth  and  level  surface. 


THE   PROPERTIES   OF   MATTER.  27 


Porosity. 

Experiment  14.  —  Pour  30  cu.  cm.  of  water  into  a  long  test-tube. 
Carefully  add  20  cu.  cm.  of  strong  alcohol,  holding  the  tube  so  that 
the  latter  may  run  down  its  side  and  rest  upon  the  water  without 
mixing  with  it.  Gently  bring  the  tube  into  a  vertical  position,  mark 
the  height  of  the  liquid  in  the  tube,  close  the  mouth  of  the  tube  with 
the  thumb,  and  thoroughly  shake  the  two  liquids  together.  Notice 
again  the  height  of  the  liquid  contents  of  the  tube.  It  looks  as  if  some 
of  the  water  and  some  of  the  alcohol  had  been  forced  into  the  same 
space,  in  spite  of  the  impenetrability  of  matter. 

Experiment  15.  —  Fill  a  glass  tumbler  with  large  shot  or  peas,  and 
then  see  how  much  well-dried  sand  or  salt  you  can  add.  Perhaps 
what  happens  here  is  analogous  to  what  happened  in  Experiment  14. 

28.  Porosity  is  that  property  of  matter  by  virtue  of  ivhich 
spaces  exist  between  the  molecules.  A  body  does  not  com- 
pletely fill  the  space  it  seems  to  occupy. 
As  a  result  of  this,  we  have  the  possi- 
bility of  an  interpenetration  of  two 
bodies,  the  molecular  volumes  of  one 
occupying  the  intermolecular  spaces  of 
the  other,  so  that  the  resultant  volume 
is  less  than  the  sum  of  the  constituent 


FIG.  9. 

volumes. 

(a)  When  iron  is  heated,  the  molecules  are  pushed  further  apart, 
the  pores  are  enlarged,  and  we  say  that  the  iron  has  expanded.  When 
a  piece  of  iron  or  lead  is  hammered,  it  is  made  smaller,  because  the 
molecules  are  forced  nearer  together,  thus  reducing  the  size  of  the 
pores.  Cavities  or  cells,  like  those  of  bread  or  sponge,  are  not  properly 
called  pores. 

29.  Strain  and  Stress. — Any  change  in  the  shape  or 
size  or  volume  of  a  solid  is  called  a  strain.  Thus,  if  a 
mass  of  metal  becomes  compressed,  or  bent,  or  twisted,  or 


28 


SCHOOL  PHYSICS. 


distorted  in  any  way,  it  is  said  to  experience  a  strain.  The 
use  of  the  word  "  strain  "  to  designate  a  force  that  pro- 
duces a  deformation  is  common  in  literature,  but  incorrect 
in  mechanics.  The  force  that  produces  a  strain  is  called 
a  stress. 

Elasticity. 

Experiment  16.  —  Squeeze  a  rubber  ball.  Stretch  a  rubber  band. 
Stretch  a  spiral  spring.  Bend  a  thin  strip  of  steel,  wood,  or  whale- 
bone. In  each  case  the  volume  or  form  is  restored  to  its  initial  condition 
when  the  distorting  force  ceases  to  act. 

Experiment  17. —  Firmly  fasten  one  end  of  a  piece  of  spring-brass 
wire,  about  No.  27  and  about  1  m.  long  (e.g.,  grip  it  in  a  hand  vise), 
so  that  the  wire  hangs  vertical.  To  the 
lower  end  of  the  wire  fasten  a  weight  of  75 
or  100  g.  To  this  weight  attach  a  pointer 
so  that  it  extends  horizontally  from  the 
direction  of  the  wire.  Turn  the  weight 
through  a  considerable  angle,  thus  twisting 
the  wire.  Release  the  weight,  and  notice  the 
rapid  movements  of  the  pointer  of  the  torsional 
pendulum. 

30.  Elasticity  is  that  property  of 
matter  by  virtue  of  which  bodies  re- 
sume their  original  form  or  size  when 
that  form  or  size  has  been  changed 
by  any  external  force.  There  is  an 
elasticity  of  volume  and  an  elasticity 
of  form  or  figure.  The  former  is 
peculiarly  a  property  of  gases  and 
liquids  ;  the  latter,  of  solids. 

FIG.  10. 

(a)  The  elasticity  of  a  body  may  be  de- 
veloped by  pressure,  by  pulling,  by  bending,  or  by  twisting. 


THE  PROPERTIES  OF  MATTER.  29 

(6)  All  bodies  possess  this  property  in  some  degree,  because  all 
bodies,  solid,  liquid,  or  aeriform,  when  subjected  to  pressure  (within 
limits  varying  with  the  substance),  will  resume  their  original  size 
upon  the  removal  of  the  pressure.  Fluids  have  no  elasticity  of  form ; 
on  the  other  hand,  all  fluids  have  perfect  elasticity  of  size.  The  ratio 
of  the  numerical  value  of  a  stress  to  the  numerical  value  of  the  strain 
produced  by  it  is  called  the  coefficient  of  elasticity. 

(c)  Solids  that  have  little  or  no  ability  to  resume  their  original 
shape  after  the  action  of  a  stress  are  said  to  be  inelastic  or  plastic.  In 
the  case  of  even  highly  elastic  solids,  when  the  strain  exceeds  a  certain 
value,  called  the  limit  of  elasticity,  the  substance  acts  like  a  plastic 
solid.  A  body  under  stress  has  reached  its  limit  of  elasticity  when 
any  further  stress  will  cause  a  permanent  alteration  of  form  or  size. 

Molecular  Attraction. 

Experiment  18.  —  Dip  a  finger  into  water.  Upon  removing  it, 
notice  that  it  is  wet,  that  water  adheres  to  it.  Hold  the  finger  point- 
ing downward,  and  notice  that  a  drop  of  water  gathers  at  the  finger 
tip.  That  drop  is  composed  of  many  particles  that  cling  together,  or 
cohere.  Something  makes  the  water  particles  cling  to  each  other  and  to 
thejinger,  in  spite  of  the  force  of  gravity. 

Experiment  19.  —  Hold  the  end  of  a  stick  of  sealing  wax  in  a  candle 
flame.  Notice  that  the  fused  drop  increases  in  size  until  it  becomes  so 
heavy  that  the  molecular  forces  can  no  longer  counteract  its  weight. 

Experiment  20.  —  Cut  a  lead  bullet  so  as  to  present  two  flat,  clean 
surfaces.     Press  the  two  parts  together  with  a  slight  twist- 
ing motion.     They  will  cling  together.     Lead  disks  are  made 
for  this  purpose.      When  used,  their  opposing  surfaces 

should  be  flat  and  bright. 

FIG. 11 

Experiment  21.  —  Take  a  sheet  of  gold  leaf  in  your  fin- 
gers, and  try  to  pick  the  metal  off  with  the  fingers  of  the  other  hand. 
Some  of  the  gold  will  stick  to  your  fingers. 

31.  Cohesion  and  Adhesion.  —  Cohesion  is  the  force  that 
holds  together  like  molecules;  adhesion  is  the  force  that  holds 
together  unlike  molecules.  The  distinction  is  traditional 
rather  than  necessary. 


30  SCHOOL  PHYSICS. 

(a)  Exhibitions  of  this  force  are  more  noticeable  in  solids  than  in 
liquids ;  in  aeriform  bodies  it  seems  to  be  wanting. 

(6)  This  is  the  force  that  holds  bodies  together,  and  gives  them 
form.  Were  its  action  suddenly  to  cease,  brick  and  stone  and  iron 
would  crumble  to  finest  powder,  and  all  our  homes  and  cities  and 
selves  fall  to  hopeless  ruin.  This  force  acts  only  at  insensible  (mo- 
lecular) distances.  Let  the  parts  of  a  body  be  separated  by  a  sensible 
distance,  and  we  say  that  the  body  is  broken.  If  the  molecules  of  the 
parts  can  again  be  brought  within  molecular  distance  of  each  other, 
cohesion  will  again  act,  and  hold  them  there.  This  may  be  done  by 
simple  pressure,  as  in  the  cases  of  wax,  freshly  cut  lead,  broken  ice, 
and  many  powders  ;  it  may  be  done  by  welding  or  melting,  as  in  the 
case  of  iron. 

32.  Hardness  is  that  property  of  matter  by  virtue  of  which 
some  bodies  resist  any  attempt  to  force  a  passage  between 
their  particles.  The  relative  hardness  of  two  substances 
is  determined  by  finding  out  which  of  them  will  scratch 
the  other ;  e.g.,  we  know  that  glass  is  harder  than  copper 
because  it  will  scratch  copper. 

(a)  The  hardness  of  many  solid  substances  is  increased  by  raising- 
the  body  to  a  high  temperature  and  suddenly  cooling  it.  The  process 
of  giving  a  body  a  suitable  degree  of  hardness  is  called  tempering. 
Some  substances,  like  copper,  are  made  softer  by  raising  to  a  high 
temperature  and  slowly  cooling.  This  process  is  called  annealing. 

Tenacity. 

Experiment  22. —  Cut  several  strips  of  manilla  paper  about  5  by 
25  cm.  Turn  each  end  of  each  strip  over,  and  fasten  the  edges  with 
glue  so  as  to  make  a  good  hem  at  each  end.  In  the  loop  at  one  end 
of  the  paper  strip  insert  a  stout  rod  the  length  of  which  exceeds  the 
width  of  the  paper  strip.  Fasten  this  rod  by  a  stout  string  or  wire 
bail  to  a  nail  in  a  board  or  table-top.  Similarly  fasten  the  other  end 
of  the  strip  to  the  hook  of  a  good  spring-balance,  held  as  shown  in 
Fig.  12.  Pull  steadily  with  the  balance  and  in"  a  line  with  its  length, 
so  as  to  avoid,  as  far  as  possible,  all  friction  of  the  sliding  bar  to 
which  the  hook  is  attached.  Watch  the  index  of  the  balance  all  the 


THE  PROPERTIES   OF  MATTER.  31 

time,  looking  directly  down  upon  it  so  as  to  avoid  the  error  of  parallax. 
Continue  to  pull  until  the  paper  breaks.  Be  careful  that  the  recoil 
of  the  hook  does  not  injure  your  hands.  Repeat  the  experiment 
with  several  similar  strips,  recording  after  each  test  the  maximum 
reading  of  the  index.  If  the  index  does  not  rest  over  the  zero 
mark  when  the  balance  is  in  a  horizontal  position,  the  proper  correc- 


FIG.  12. 

tion  should  be  made  for  each  reading  taken.  The  average  of  these 
several  readings  will  be  a  fair  expression  of  the  strength  of  the  paper. 
Make  a  similar  series  of  tests  with  similar  strips  of  paper  twice  as 
wide.  Compare  the  two  average  results.  From  your  data,  compute 
the  strength  of  a  strip  2.2  cm.  wide  and  experimentally  verify  the 
result. 

33.  Tenacity  is  that  property  of  matter  by  virtue  of  ivhich 
some  bodies  resist  a  force  tending  to  pull  their  particles 
asunder.  Its  measure  is  the  ratio  between  the  breaking 
weight  and  the  area  of  the  cross-section  of  the  body 
broken.  It  varies  with  different  substances,  with  the  form 
of  the  body,  with  the  temperature,  and  with  the  dura- 
tion of  the  pull. 

(a)  Like  hardness  and  other  characteristic  properties  of  matter, 
tenacity  is  a  variety  of  cohesion.  For  any  given  material,  it  has  been 
found  that  tenacity  is  proportional  to  area  of  cross-section;  e.g.,  a  rod 


32  SCHOOL  PHYSICS. 

with  a  sectional  area  of  a  square  inch  will  carry  twice  as  great  a  load 
as  a  rod  of  the  same  material  with  a  sectional  area  of  a  half  square 
inch ;  a  rod  10  cm.  in  diameter  will  carry  four  times  as  great  a  load 
as  a  similar  rod  5  cm.  in  diameter.  The  explanation  of  this  is  simple. 
Imagine  these  rods  to  be  cut  across,  and  it  will  be  evident  that  on 
each  side  of  the  cut  the  first  rod  will  expose  twice  as  many  molecules 
as  will  the  second,  and  that  the  third  will  expose  four  times  as  many 
as  the  fourth.  But,  for  the  same  material,  each  molecule  has  the 
same  attractive  force.  Doubling  the  number  of  these  attractive  mole- 
cules, which  is  done  by  doubling  the  sectional  area,  doubles  the  total 
attractive  force,  which,  in  this  case,  is  called  tenacity ;  quadrupling 
the  sectional  area  quadruples  the  tenacity ;  etc.  Hence  the  law. 

34.  Malleability  is  that  property  of  matter  by  virtue  of 
which  some  bodies  may  be  rolled  or  hammered  into  sheets. 

(a)  Steel  has  been  rolled  into  sheets  thinner  than  the  paper  upon 
which  these  words  are  printed.  Gold  is  the  most  malleable  metal, 
and,  in  the  form  of  gold  leaf,  has  been  beaten  so  thin  that  300,000 
sheets,  placed  one  upon" the  other,  measured  but  an  inch  in  height. 

Ductility. 

Experiment  23.  —  Heat  the  middle  of  a  piece  of  glass  tubing  about 
6  inches  long  in  an  alcohol  flame  until  red-hot.  Roll  the  ends  of 
the  glass  slowly  between  the  fingers,  and,  when  the  heated  part  is  soft, 
quickly  draw  the  ends  asunder.  That  the  fine  glass  wire  thus  produced 
is  still  a  tube,  may  be  shown  by  blowing  through  it  into  a  glass  of 
water,  and  noticing  the  bubbles  that  will  rise  to  the  surface. 

35.  Ductility  is  that  property  of  matter  by  virtue  of  which 
some  bodies  may  be  drawn  into  wire. 

(a)  Platinum  wire  has  been  made  j^-^  of  an  inch  in  diameter. 
Glass,  when  heated  to  redness,  is  very  ductile. 

(6)  Malleability  and  ductility  are  closely  related,  so  that  most 
substances  that  have  great  malleability  also  have  high  ductility.  But 
this  rule  is  not  universal ;  lead  and  tin  are  very  malleable,  but  only 
slightly  ductile. 

(c)   Ductility  involves  tenacity ;  i.e.,  although  a  substance  may  be 


THE   PROPERTIES  OF  MATTER.  33 

tenacious  without  being  ductile,  it  cannot  be  ductile  without  being 
tenacious.  The  tenacity  of  most  metals  is  increased  by  the  process  of 
wiredrawing.  Cables  made  of  twisted  iron  or  steel  wires  are  stronger 
than  iron  chains  or  rods  of  equal  weight  and  length.  Steel  wire  with 
a  tenacity  of  more  than  92  tons  per  square  inch  of  cross-section  has 
been  made,  and  wire  with  a  tensile  strength  of  70  or  80  tons  per 
square  inch  is  readily  procurable. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc. — A  decimeter  rule  divided  to  0.2  mm. ; 
a  diagonal  scale ;  dividers  (see  Fig.  13)  ;  wire ;  wire  gauge  (see  Fig.  14)  ; 
calipers  (see  Figs.  15  and  16)  ;  a  solid  cylinder ;  a  metal 
tube;  a  tumbler;  tin  can;  a  glass  vessel  graduated  to 
0.1  cu.  cm.;  wooden  blocks,  rods,  and  bars;  clevis;  a  tin- 
can  cover  for  scale-pan ;  two  pieces  of  |-inch  gas-pipe  each 
4  inches  long ;  a  straightedge ;  a  wheat  straw ;  two  small 
vises ;  sand-bag  weights ;  soldering  tools  and  materials ; 
cutting  pliers. 

1.  What  is  the  length  of  a  full  line  as  printed  in  this 
book?     Place  the  graduated  edge  (not  the  side)  of  the 
decimeter  rule  on  the  paper,  with  some  plainly  visible 
mark,  as  0.5  or  1  cm.  (not  the  end  of  the  rule),  at  one  end 

of  the  printed  line.     Always  use  a  rule  in  this  way  for      '         ' 
accurate  measurements. 

2.  Draw  on  paper  three  straight  lines  with  lengths  of  2.57  inches, 
3.34  inches,  and  6.4  centimeters  respectively. 

3.  Tightly  pinch  the  leaves  of  this  book  (inside  the  covers)  between 
two  small  blocks  that  come  flush  with  them  at  the  top.    Remove  some 
of  the  leaves  so  that  those  that  remain  make  a  layer  just  1  cm.  thick. 
Count  the  leaves,  and  compute  in  decimals  of  a  millimeter  the  thick- 
ness of  an  average  leaf  of  this  book. 

4.  Determine  the  gauge  numbers  of  four  pieces  of  wire.      Use  the 
notches  around  the  edge  of  the  steel  plate,  and  not  the  larger  circular 
openings  at  the  inner  end  of  the  notches.     If  you  have  a  micrometer 
caliper,  determine  the  diameter  of  each  piece.     The  best  wire  gauge 
to  use  is  that  known  as  the  Brown  and  Sharpe,  "  B  &  S."     Introduce 
the  wire  into  the  slit  which  admits  it  with  a  very  slight  pressure,  and 
note  the  number  corresponding  to  that  slit.     Be  sure  that  the  wire  is 
not  rusty,  dirty,  or  bruised  at  the  point  where  it  is  gauged.     It  is 
convenient  to  buy  such  wire  wound  on  spools.  . 

3 


34 


SCHOOL  PHYSICS. 


FIG.  14. 


5.  Wind  25  turns  of  No.  30  annealed  wire  around  a  cylinder  an  inch 
or  more  in  diameter,  being  careful  that  the  successive  turns  are  as 

close  as  possible  to  each 
other.  Measure  the 
total  width  of  the  wire 
band  on  the  cylinder, 
and  compute  the  di- 
ameter of  No.  30  wire. 
Compare  your  result 
with  the  table  given  in 
the  appendix. 

6.  With  the  outside 
calipers,    measure    the 
diameter    of    the   iron 
ball  used  in  Exercise  6 
on  p.  24.     Compare  the 
result    then     obtained 
and   recorded   in   your 
notebook  with  that  now 
found. 

7.  Measure    the    di- 
ameter and  length  of  a  small  cylinder.     If,  by  measuring  the  rod  at 
short  intervals  with  the  calipers,  you  find  that  its  diameter  is  not 
uniform,   use    the   average    of   your   several 

measurements,  (a)  Compute  the  surface  area 
of  the  cylinder.  (&)  Compute  the  volume  of 
the  cylinder. 

8.  Measure  the  length  and  the  inside  and 
outside  diameters  of  a  metal  tube.  If  you 
have  no  inside  calipers,  bend  a  piece  of  an- 
nealed wire  into  a  V-shape,  and  use  that, 
(a)  Compute  the  total  surface  area  of  the  tube. 

volume  of  metal  in  the  tube,  (c)  Test 
your  result  by  the  displacement  of  water. 
9.  (a)  With  the  inside  calipers,  meas- 
ure the  diameter  of  the  tumbler  on  the 
inside,  at  the  bottom  and  at  the  top. 
From  these  measurements  determine  the 
average  diameter  of  the  tumbler.  Place  a  straightedge  across  the  top 
of  the  tumbler  in  the  line  of  a  diameter.  Measure  the  perpendicular 


FIG.  15. 


Compute  the 


FIG.  16. 


THE   PROPERTIES   OF   MATTER.  35 

distance  from  the  bottom  of  the  tumbler  to  the  under  side  of  the 
straightedge.  Compute  the  capacity  of  the  tumbler  in  cubic  centi- 
meters. (6)  Fill  the  tumbler  with  water  and  pour  the  water  into 
the  graduate,  and  thus  test  the  accuracy  of  your  previous  measure- 
ments and  computation. 

10.  Using  the  wire  gauge,  select  coils  of  No.  30  wire,  brass,  copper, 
iron,  and  steel.  From  each  coil  cut  oif  two  pieces  each  about  1  m. 
long.  Wrap  one  end  of  a  wire  twice  about  the  middle  of  a  piece  of 
gas-pipe,  and  fasten  by  twisting  the  end  around  the  body  of  the  wire, 
being  careful  not  to  make  any  kink  in  the  body  of  the  wire.  Similarly 
fasten  the  other  end  of  the  wire  to  the  other  piece  of  gas-pipe.  Through 
each  piece  of  gas-pipe  pass  a  60  cm.  piece  of  wire  much  stouter  than 
the  No.  30  iron  or  steel,  bend  these  wires  sharply  at  the  ends  of  the 
gas-pipe,  and  twist  the  ends  together  so  as  to  make  a  bail  in  the  shape 
of  an  isosceles  triangle  of  which  .the  pipe  shall  be  the  shorter  side. 
From  one  of  these  bails  suspend  a  tin  can  or  basin  (the  weight  of 
which,  with  its  bail  and  gas-pipe,  has  been  ascertained) ;  support  the 
other  bail  so  that  the  can  shall  be  only  a  few  inches  above  the  floor  or 
table.  Place  a  weight  of  200  or  300  g.  in  the  pan,  and  add  weights 
of  10  or  5  g.  each  until  the  load  breaks  the  wire.  In  like  manner 
determine  the  breaking  strength  of  the  other  piece  of  the  same  kind 
of  wire.  Make  like  tests  with  the  other  kinds  of  wire.  Tabulate 
your  results  in  some  such  way  as  the  following:  — 


BREAKING  STRENGTH  OF  Xo.  30  WIRE. 

Copper.  Brass.  Iron.  Steel. 


First  test  . 
Second  test 
Averages  . 


11.  Provide  two  pieces  of  hard  wood,  A  and  B,  and  place  them  on 
the  table  as  shown  in  Fig.  17,  with  their  ridges  parallel,  and  a  meter 
apart.  Upon  these  blocks  place  a  wrooden  bar,  W,  1.2  cm.  (£  in.)  square 
and  about  104  cm.  long.  Midway  between  the  supporting  ridges 
place  a  small  clevis,  C,  made  of  sheet  metal  and  carrying  a  scale-pan. 
In  some  cases  it  may  be  convenient  to  pass  the  string  through  a  hole 
in  the  table,  so  that  the  scale-pan  will  hang  below  the  table-top.  Pro- 
vide a  straightedge  a  meter  long,  and  faced  on  the  edge  at  each  end 
with  metal  of  the  same  thickness  as  the  clevis.  Place  the  straight- 


36  SCHOOL  PHYSICS. 

edge  on  W,  with  its  ends  over  the  ridges  of  A  and  B.     If  there  is  no 
deflection  or  "  sag  "  in  W,  the  straightedge  will  just  touch  the  upper 

surface  of  C ;  otherwise 
the  distance  between  C 
and  the  straightedge 
will  measure  the  deflec- 
tion. Place  a  known 
weight- (say,  100  g.)  in 
the  scale-pan,  and  to 
this  weight  add  the 
weight  of  the  clevis  and 
FIG.  17.  the  scale-pan,  and  call 

the  sum  the  load.  Meas- 
ure the  deflection  of  W  caused  by  the  load.  Double  the  load,  and 
measure  the  deflection  thus  caused.  Record  these  data. 

For  quick  work,  each  end  of  a  cord  or  annealed  wire  may  be 
fastened  to  the  knob  of  a  known  weight,  and  the  cord,  thus  loaded, 
placed  across  the  middle  of  the  bar. 

Instead  of  measuring  the  deflection  thus  directly,  using  a  straight- 
edge, the  deflection  may  be  magnified  and  more  easily  read  in  this 
way :  Solder  a  pin  to  the  further  end  of  the  clevis  so  that  it  shall 
project  horizontally  and  at  right  angles  to  the  length  of  the  wooden 
bar.  Select  a  straight  straw  30  cm.  or  more  in  length.  Trim  the 
smaller  end  of  the  straw  so  that  it  may  act  as  a  pointer  or  index. 
Thrust  a  needle  through  the  straw  a  little  less  than  five-sixths  of  its 
length  from  the  pointed  end.  Measure,  from  the  needle  toward  the 
nearer  end  of  the  straw,  a  distance  just  one  fifth  the  length  of  the  part 
on  the  other  side  of  the  needle,  and  mark  the  point  thus  located  by  a 
pen  mark  on  the  straw.  Thrust  the  end  of  the  needle  carrying  the 
straw  into  the  cork  of  a  bottle  so  that  the  needle  shall  be  horizontal 
when  the  bottle  is  upright.  Place  the  bottle  so  that  the  height  of  the 
needle  shall  be  a  little  less  than  that  of  the  pin  carried  by  the  clevis, 
while  the  straw  is  parallel  with  the  wooden  bar.  Adjust  the  bottle  so 
that  the  ink  mark  shall  come  under  the  pin  on  the  clevis.  Tie  or  tack 
any  convenient  graduated  scale  so  that  it  shall  stand  on  end  against 
the  vertical  face  of  a  block,  and  set  it  so  that  the  index  end  of  the 
straw  shall  stand  opposite  one  of  the  marks  near  the  bottom  of  the 
scale.  This  mark  is  to  be  considered  the  zero  mark.  A  deflection  of 
1  cm.  at  the  middle  of  the  bar  will  move  the  index  over  5  cm.  of  the 
scale.  Read  deflections  from  the  edge  of  the  scale.  After  each  weigh- 
ing, see  whether  the  index  returns  to  the  zero  of  the  scale  or  not. 


THE   PROPERTIES   Otf  MATTER.  37 

Replace  W  by  another  bar  made  of  the  same  kind  of  wood,  with 
the  same  length  and  thickness,  but  2.4  cm.  wide.  Load  it  to  produce 
the  same  deflections  as  before,  and  record  the  data.  In  similar  man- 
ner try  the  narrow  bar  with  the  supports  0.5  m.  apart,  and  the  broad 
bar  on  edge  with  the  supports  1  m.  apart.  From  all  the  data  thus 
obtained  and  recorded,  concerning  the  stiffness  of  beams  carrying 
loads  midway  between  their  supports,  answer  the  following  questions: 
What  is  the  relation  between  the  load  and  the  deflection?  Between 
the  length  of  the  beam  and  the  deflection?  Between  the  breadth  of 
the  beam  and  the  deflection?  Between  the  thickness  of  the  beam 
and  the  deflection  ? 

12.  Experimenting  with  wooden  rods  of  different  lengths,  widths, 
and  thicknesses,  supported  at  their  ends  and  loaded  in  the  middle, 
show  that  the  breaking  strength  varies  directly  as  the  width  and  as 
the  square  of  the  thickness,  and  inversely  as  the  length,  or  that  it  does 
not ;  i.e.,  verify  or  disprove  the  formula :  — 

Breaking  strength  oo  — . 

(The  sign  co  is  read  "varies  as  "  or  "is  proportional  to.") 

13.  Grip  one  end  of  a  small  straight  wire,  a  yard  or  so  in  length, 
in  a  small  vise.     Support  the  vise  firmly,  so  that  the  wire  may  hang 
vertically.      Grip  the  free  end  of  the  wire  in  another  small  vise  of 
known  weight.     Near  the  lower  end  of  the  wire,  fix  a  horizontal 
pointer  (a  stiff  bristle  stuck  on  with  shoemaker's  wax  will  answer), 
and  mark  its  level  on  a  card  fixed  upright.     Call  this  level  the  zero  of 
the  card  scale.     Add  a  sand  bag  of  the  same  weight  as  the  vise,  and 
mark  the  level  of  the  pointer  on  the  card.     Remove  the  sand  bag  and 
see  if  the  pointer  comes  back  to  zero.     Add  sand  bags  or  equal 
weights  in  succession,  marking  the  successive  levels  of  the  pointer 
on  the  scale,  removing  the  weights  after  each  trial,  and  giving  the 
pointer  a  chance  to  return  to  the  zero  mark.     When  you  find  that 
the   wire  has  been   permanently   stretched,  stop  the  test.      Record 
the  elongation    after  each  weight.      Repeat  with   a  similar  wire, 
twice  as  long.     Can  you  discover  any  law  for  the  stretching  of  wire  ? 
If  so,  record  it.     Verify  that  law  by  similar  experiments  with  other 
wires. 

14.  Using  a  rod  of  clear  ash,  36  inches  long  and  half  an  inch 
square,  determine  the  relation  between  the  force  used  to  twist  the 
rod  and  the  amount  of  torsion  produced;    i.e.,  if  a  certain  force 
produces  a  torsion  of  5°,  how  much  torsion  will  twice  that  force 
produce  ? 


38  SCHOOL  PHYSICS. 

15.  Using  the  same  rod  or  a  similar  one,  determine  the  relation 
between  the  length  of  the  rod  and  the  amount  of  the  torsion. 

16.  Using  the  same  rod  and  one  of  the  same  kind  of  wood  and  the 
same  length,  but  |  of  an  inch  square,  verify  the  statement  that  torsion 
varies  as  ^j,  d  representing  the  diameter  of  the  rod.     How  does  the 
formula  as  given  agree  with  the  statement  that  the  torsion  varies 
inversely  as  the  square  of  the  cross-section. 


III.     THE   THREE   CONDITIONS   OF  MATTER,   ETC. 

36.  Conditions  of  Matter. — Matter  exists  in  three  con- 
ditions or  forms,  —  the  solid,  the  liquid,  and  the  aeriform. 
Liquid  and  aeriform  bodies  are  fluids. 

37.  A  Solid  is  a  body  whose  molecules  change  their  rela- 
tive positions  with  difficulty.     Such  bodies  have   a  strong 
tendency  to  retain  any  form  that  may  be  given  to  them, 
and  can  sustain  pressure  without  being  supported  laterally. 
A  movement  of  one  part  of  such  a  body  produces  motion 
in  all  of  its  parts. 

38.  A  Fluid   is   a   body   whose   molecules  easily  change 
their   relative  positions.      Fluids   cannot  sustain  pressure 
without  being  supported  laterally.      The  term   compre- 
hends liquids,  gases,  and  vapors. 

i 

Cohesion  of  Liquids. 

Experiment  24.  —  Suspend  a  clean  glass  plate  of  about  four  inches 
area  from  one  end  of  a  scale-beam,  and  accurately  balance  the  same 
with  weights  in  the  opposite  scale-pan.  The  supporting  cords  may 
be  fastened  to  the  plate  with  wax.  Beneath  the  plate  place  a  saucer 
so  that  when  the  saucer  is  filled  with  water  the  plate  may  rest  upon 
the  liquid  surface,  the  scale-beam  remaining  horizontal.  Be  sure  that 
there  are  no  air-bubbles  under  the  plate.  Carefully  add  small  weights 
to  those  in  the  scale-pan.  Notice  that  the  water  beneath  the  plate  is 


THE  THREE   CONDITIONS  OF  MATTER.  39 

raised  above  its  level.  Add  more  weights  until  the  plate  is  lifted 
from  the  water.  ^Notice  that  the  under  surface  of  the  plate  is  wet. 
These  molecules  on  the  plate  have 
been  torn  from  their  companions  in 
the  saucer,  the  adhesion  between  the 
water  and  the  plate  being  greater 
than  the  cohesion  of  the  water. 
The  weights  added  to  the  original 
counterpoise  were  needed  to  over- 
come the  cohesion  of  the  water 
molecules. 

39.  A  Liquid  is  a  body  ivhose  FlG  18 
molecules    easily   change    their 

relative  positions,  yet  tend  to  cling  together.  Such  bodies 
adapt  themselves  to  the  form  of  the  vessel  containing 
them,  but  do  not  retain  that  form  when  the  restraining 
force  is  removed.  Their  free  surfaces  are  always  hori- 
zontal. Water  is  the  best  type  of  liquids. 

40.  An   Aeriform  Body   is  one  whose    molecules    easily 
change  their  relative  positions,  and  tend  to  separate  from 
each  other  almost  indefinitely.      Such   bodies   are  of   two 
kinds,  —  gases  and  vapors.     Gases  remain  aeriform  (i.e., 
retain  the  form  of  air)  under  ordinary  conditions,  while 
vapors  resume  the  solid  or  liquid  form  at  ordinary  tem- 
peratures.    Atmospheric  air  is  the  most  familiar  type  of 
aeriform  bodies. 

41.  Changes  of  Condition.  —  Many  substances,  like  iron 
and  gold  and  water,  may  be  made  to  exist  in  all  of  these 
three  forms  by  suitable  adjustments  of  temperature  and 
pressure.     The  identity  of  ice,  water,  and  steam,  is  fa- 
miliar to  all. 

(a)  Experiments  with  electric  discharges  in  high  vacuums  have 


40  SCHOOL  PHYSICS. 

given  results  which,  in  the  minds  of  many,  prove  the  existence  of  a 
fourth  condition  of  matter.  For  matter  in  this  extremely  thin  or 
attenuated  form,  the  name  "  radiant  matter  "  has  been  proposed. 

Solution. 

Experiment  25. — Into  a  beaker  half  full  of  water,  drop  a  few  lumps 
of  sugar.  Stir  the  contents  of  the  glass  until  the  solid  disappears. 

Experiment  26.  —  Mix  50  g.  of  pulverized  ammonium  nitrate  arid 
25  g.  of  pulverized  ammonium  chloride  (sal-ammoniac).  Put  the 
mixture  into  75  cu.  cm.  of  cold  water  in  a  beaker,  and  stir  the  sub- 
stances together  with  a  small  test-tube  containing  a  little  cold  water. 
Notice  that  the  solids  disappear.  Carefully  observe  the  condition  of 
the  water  in  the  test-tube. 

42.  Solution  is  the  transformation  of  matter  from  the  solid 
or  gaseous  form  to  the  liquid  form  by  means  of  a  liquid  called 
the  solvent  or  menstruum.  The  process  is  essentially  a 
change  of  molecular  condition.  When  the  change  is 
from  the  solid  to  the  liquid  form,  there  is  an  absorption 
of  heat  with  a  consequent  fall  of  temperature,  as  is  strik- 
ingly seen  in  freezing  mixtures.  The  solution  of  a  gas 
in  a  liquid  is  accompanied  by  a  release  of  heat  and  a  con- 
sequent rise  of  temperature.  When  the  solvent  has  dis-' 
solved  as  much  of  a  given  substance  as  it  can,  the  solution 
is  said  to  be  saturated. 

(a)  The  solubility  of  any  solid  in  any  liquid  is  constant  at  a  given 
temperature,  and  may  be  determined  by  experiment.  The  solubility 
of  any  gas  is  also  constant  under  the  same  conditions ;  it  varies  with 
temperature,  pressure,  and  the  nature  of  the  solvent.  With  a  mix- 
ture of  gases,  each  is  dissolved  in  the  same  quantity  as  if  it  were 
present  alone,  and  under  the  same  pressure  as  in  the  mixture. 

Crystallization. 

Experiment  27.  —  Dissolve  about  a  quarter  of  a  pound  of  alum  in 
a  pint  of  hot  water.  Hang  several  strings  in  the  solution,  and  set 


THE  THKEE  CONDITIONS  OF  MATTER.  41 

the  vessel  containing  it  aside  for  the  night.  In  the  morning  notice 
the  regularity  and  similarity  of  the  crystals  that  have  formed  on  the 
strings. 

43.  Crystallization.  —  Many  solids  forming  slowly  from 
the  liquid  or  aeriform  condition,  and  thus  haying  great 
freedom  of  molecular  motion,  assume  regular  forms,  with  a 
certain  number  of  plane  surfaces  symmetric- 
ally arranged,  and  with  a  definite  internal  struc- 
ture. Such  bodies  are  called  crystals.  Thus 
quartz  crystallizes  in  hexagonal  prisms  termi- 
nated by  hexagonal  pyramids. 


(a)  The  internal  structure  is  exhibited  in  the  cleavage, 
and  in  the  appearance  of  sections  cut  from  the  crystal 
and  viewed  by  polarized  light.  The  planes  of  cleavage 
are  certain  definite  planes  along  which  separation  is  most 
easily  effected. 

(£>)  The  form  and  structure  of  crystals  are  of  great  importance  to 
the  chemist  and  the  mineralogist,  as  the  nature  of  many  substances 
may  be  ascertained  thereby.  (See  definition  of  "  crystallography  "  in 
"  The  Century  Dictionary.") 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Bottles  containing  concentrated  solu- 
tions of  potassium  nitrate  (saltpeter)  and  of  ammonium  chloride 
(sal  ammoniac) ;  several  pieces  of  window  glass  4  or  5  inches  square ; 
a  magnifying  lens,  preferably  mounted  (the  glasses  used  in  botanical 
study  will  answer  admirably);  a  Bunsen  or  an  alcohol  lamp;  test- 
tube  ;  iodine  ;  Hessian  crucible ;  brimstone ;  saucer ;  bottle ;  round  or 
'•  rat-tail "  file ;  Florence  flask  ;  corks  and  cork-borers ;  glass  tubing ; 
retort-stand ;  two  plain  tumblers  of  thin  glass  and  of  the  same  size ; 
waste- jar. 

1.  (a)  Slowly  warm  a  piece  of  thoroughly  cleaned  glass  over  the 
lamp ;  hold  the  glass  horizontal,  and  pour  a  little  of  the  solution  of 
saltpeter  upon  it.  Move  the  glass  quickly  so  as  to  spread  the  liquid 
over  its  surface,  and  then,  hold  it  over  the  waste-jar  so  as  to  drain  off 
the  surplus*  solution.  When  a  cloudy  patch  appears  on  the  glass, 
examine  it  carefully  through  the  lens,  make  a  drawing  of  what  you 
see,  and  label  it  "  KNO3  Crystals." 


42  SCHOOL  PHYSICS. 

(&)  Take  a  similar  course  with  the  other  solution,  and  label  the 
drawing  «  NH4C1  Crystals." 

2.  Drop  a  single  crystal  of  iodine  into  the  bottom  of  a  test-tube 
(Fig.  20),  and  heat  it  gently.     After  the  tube  has  been  well  filled 
with  the  beautiful  iodine  vapor,  allow  it  to  cool.      With  a 
p|    magnifying  lens,  examine  the  iodine  crystals  that  form  on  the 
walls  of  the  test-tube. 

3.  Melt  about  200  g.  of  sulphur  (brimstone)  in  a  Hessian 
crucible  (Fig.  21),  and  allow  it  to  cool  until  a  crust  forms  over 
it.  Through  a  hole  pierced  in  this  crust,  pour  out  the  still 
liquid  sulphur.  When  the  crucible  is  cool,  break  it,  and  with 
a  magnifying  glass  examine  the  needle-shaped  sulphur  crystals 
with  which  it  is  lined.  The  crucible  may  be  saved  by  pouring 
all  of  the  melted  sulphur  into  a  pasteboard  box,  and  allowing 
'  the  crystals  to  form  there. 

4.  Fill  a  clear  glass  tumbler  with  fresh  hydrant  or  well  water.     Fill 
a  similar  vessel  with  water  that  has  recently  been  wTell  boiled.     Set 
both  in  a  moderately  warm,  quiet  place,  and  let  them 

stand  over  night.  Examine  the  walls  of  the  two 
tumblers,  and  account  for  the  difference  in  their 
appearance. 

5.  With  a  round  file,  work  a  notch  in  the  edge  of 
a  saucer,  and  a  hole  about  a  centimeter  in  diameter 
in  the  middle  of  the  bottom.     Invert  the  saucer  in 

an  earthenware  or  tin  pan,  and  cover  it  with  water.  FlG  2i. 

Fill  a  bottle  with  water,  and  stand  it  upside  down 

with  its  mouth  around  the  hole 
in  the  saucer.  Fill  a  Florence 
flask  with  water,  and,  holding 
it  under  water,  close  its  mouth 
with  a  cork  carrying  a  bent 
glass  delivery-tube.  Keeping 
the  flask  and  tube  full  of 
water,  thrust  the  free  end  of 
the  tube  through  the  notch  in 
the  edge  of  the  saucer,  and 
FlG  22  place  the  flask  on  the  retort- 

stand.    Be  sure  that  flask,  tube, 

and  bottle  are  full  of  water.     Heat  the  flask  carefully  until  the  water 

has  boiled  for  several  minutes.     The  collection  bottle  will  be  found  to 


THE   THREE   CONDITIONS   OF  MATTER. 


43 


contain  something  besides  water  ;  it  is  air.  Can  you  imagine  whence 
it  came  ?  Repeat  the  experiment  with  water  that  has  been  recently 
boiled  in  an  open  vessel.  Do  you  collect  any  air  now  ?  Perhaps  the 
boiling  of  water  expels  air  that  it  holds  in  solution.  Think  about  it. 
Has  your  work  given  you  any  information  as  to  the  solubility  of  air 
in  water  ?  As  to  the  porosity  of  water  ? 

Superficial  Molecules. 

Experiment  28.  —  Fill  a  tumbler  brimming  full  of  water.     With 
a  pipette  (Fig.  23),  add  more  water,  drop  by  drop  and  patiently,  until 
the  water  in  the  tumbler  is  actually  heaped  up  higher 
than  the  edges  of  the  glass.     Try  to  imagine  an  invisi- 
ble skin  stretched  over  the  liquid  surface  to  keep  it 
from  overflowing  the  edge  of  the  tumbler. 

Experiment    29. —  Carefully    place   a   fine    sewing 
needle  upon  the  surface   of  water.     With  care,  and 
perhaps  repetition,  the  needle 
may  be  made  to  float.     If  you 
have  serious  trouble  in  mak- 
FIG.  24.  ing  ik  float,  draw  it  between 

the  fingers  or  wipe  it  with  an 

oily  cloth.     A  hair-pin  bent  slightly  near  the  tips  may 
be  used  to  lower  the  needle  so  that  neither  end  shall          FIG<  23. 
touch  the  water  before  the  other.     Closely  examine 
the  surface  of  the  water.     Notice  that  the  needle  rests  in  a  little 
depression  or  bed,  just  as  it  would  if  the  surface  of  the  water  was 
a  thin  skin  or  membrane. 

Experiment  30. — Blow  a  soap-bubble  without  detaching  it  from  the 
pipe  or  tube.  Leave  the  tube  open,  and  notice  that  the  film  contracts, 
diminishing  the  size  of  the  bubble,  and  expelling  some  of  the  air  from 
it.  The  current  of  air  from  the  interior  of  the  bubble  may  be  made 
to  deflect  the  flame  of  a  candle. 

Experiment  31.  —  Float  two  sewing  needles  on  the.  surf  ace  of  water 
about  a  quarter  of  an  inch  apart,  and  let  a  drop  of  alcohol  fall  upon 
the  water  between  them.  Notice  that  the  needles  separate  as  if  they 
had  been  supported  on  a  stretched  membrane,  and  the  membrane  had 
been  cut  so  that  its  parts  might  separate,  each  carrying  its  needle 
with  it. 


44  SCHOOL  PHYSICS. 

Experiment  32.  —  Drop  a  few  small  pieces  of  camphor  upon  the 
surface  of  clean,  warm  water.  Notice  their  peculiar  gyratory  motions. 

Experiment  33.  —  Moisten  a  small  bit  of  paper,  and  stick  it  to  the 
concave  side  of  a  watch  crystal  near  the  edge,  as  an  indicator.  Dip 
the  part  of  the  convex  surface  on  the  side  indicated  by  the  paper  into 
alcohol,  so  that  not  more  than  a  sixth  of  the  rim  shall  be  wet.  Hold- 
ing the  crystal  so  that  the  adhering  drop  of  alcohol  shall  be  under  the 
paper  bit,  float  it  on  the  surface  of  a  shallow  dish  of  water  a  foot  or 
more  in  diameter.  The  glass  will  skim  across  the  surface  of  the  water 
with  the  segment  that  was  wet  with  alcohol  astern. 

44.  Superficial  Films.  —  The  molecular  forces  of  a  liquid 
are  strikingly  manifested  at  its  surface,  so  that  every  liquid 
may  be  regarded  as  bounded  by  a  superficial  film.     This 
film  is  physically  different  from  the  interior  of  the  liquid 
mass,  and  is  a  seat  of  energy.     Two  of  the  properties  of 
these  films  are  called  surface  viscosity  and  surface  tension. 

45.  Surface  Viscosity.  —  The  superficial  film  of  a  liquid 
is,  as  a  rule,  exceedingly  viscous  as  compared  with  the  inte- 
rior mass.    It  is  comparatively  hard  to  move  or  break.     To 
this  toughness  of  the  superficial  film,  the  floating  of  a 
needle  or  the  walking  of  an  insect  on  water  must  in  part 
be  ascribed,  for  the  depth  of  the  dimple  is  not  sufficient  to 
account  for  the  support  afforded  to  so  heavy  a  body.     A 
solution  of  soap  in  water  has  greater  surface  viscosity  than 
has  pure  water,  hence  its  adaptability  to  the  formation  of 
bubbles. 

(a)  The  surface  viscosity  of  a  solution  of  gum  arabic.  is  sufficient 
to  enable  frothiug  when  the  solution  is  shaken,  but  not  enough  for 
the  formation  of  bubbles ;  that  of  water  is  so  little  that  pure  water 
will  not  froth;  and  that  of  alcohol  is  so* eminently  feeble  that  alcohol 
is  often  used  in  pharmacy  to  mix  with  superficially  viscous  liquids  for 
the  purpose  of  checking  or  preventing  frothing.  To  the  same  prop- 
erty is  attributed  the  smoothing  of  a  rough  sea  by  pouring  oil  upon 


THE   THREE   CONDITIONS   OF   MATTER. 


45 


it.    The  new  surface  is  comparatively  rigid,  and  is  not  so  easily  broken 
into  surf. 

46.  Surface  Tension.  —  Experiments  show  that  a  liquid 
surface  (as  the  surface  that  separates  waterfront  air,  or  oil 
from  water)  is  in  a  state  of  tension  similar  to  that  of  a  mem- 
brane stretched  equally  in  all  directions.  This  tension  is 
practically  independent  of  the  form  of  the  surface.  It 
depends  on  the  nature  and  temperature  of  the  liquid, 
diminishing  as  the  temperature  rises.  Pure  water  has 
a  surface  tension  higher  than  that  of  any  other  substance 
that  is  liquid  at  ordinary  temperatures,  except  mercury ; 
hence  the  mixture  of  any  other  liquid  with  water  lessens 
the  surface  tension  of  the  water,  as  was  shown  in  Experi- 
ments 31  and  33. 

(a)  In  a  liquid  film,  such  as  a  soap-bubble,  "  it  is  possible  that  no 
part  of  the  liquid  may  be  so  far  from  the  surface  as  to  have  the  poten- 
tial and  density  corresponding  to  the  interior  of  a  liquid  mass;"  i.e.,  the 
film  may  be  mostly  surface.  The  exterior  and  the  interior  surfaces  of 

the  bubble  act  like  two 

sheets  of  india-rubber 

stretched    equally    in 

length    and    breadth. 

Their  tendency  to  con- 
tract forces   air  from 

the  interior  of  the  bub- 
ble,   and    repays    the 

work    performed,     or 

energy    expended,    in 

increasing  the  surfaces 

when  the  bubble  was 

blown. 

Surface  tension  may 

be  studied  under  very 
favorable  conditions  by  using  soap  or  collodion  films.     If  a  rough- 
ened ring  is  dipped  into  a  strong  solution  of  Castile  soap,  to  which 


FIG.  25. 


FIG.  26. 


46  SCHOOL  PHYSICS. 

glycerin  has  been  added,  a  plane  film  will  be  found  stretched  across 
it.  To  such  a  ring,  tie  a  loop  of  thread  and  secure  another  film,  as 
shown  in  Fig.  25.  With  a  hot  wire,  puncture  the  film  inside  the 
thread  loop,  and  the  tension  of  the  film  will  pull  the  thread  outward 
in  all  directions,  as  shown  in  Fig.  26.  Such  films  may  be  made  to 
stretch  themselves  in  singularly  beautiful  forms  on  wire  skeletons  of 
cubes,  pyramids,  cylinders,  etc. 

(6)  The  tension  of  the  superficial  film  tends  to  reduce  the  contained 
liquid  to  the  form  that  gives  the  greatest  volume  with  the  least  area 
of  surface ;  hence  the  spherical  form  of  soap-bubbles,  air-bubbles 
in  water,  raindrops,  shot,  etc.  The  various  forms  assumed  by  liquid 
masses  under  the  influence  of  surface  tension  are  conveniently  studied 
by  relieving  them  of  the  influence  of  gravity  by  floating  them  in 
liquids  of  their  own  density,  and  with  which  they  will  not  mix. 
Thus,  one  may  make  a  mixture  of  alcohol  and  water  of  the  same 
density  as  olive  oil.  Masses  of  olive  oil  placed  in  such  a  mixture  will 
neither  rise  nor  sink.  If  left  free,  they  will  assume  the  globular  form. 
When  limiting  conditions  are  imposed  upon  them,  they  assume  geo- 
metrical forms  of  great  interest,  all  having  the  smallest  superficial 
area  possible  under  the  conditions  imposed. 

(c)  When  camphor  floats  on  water,  solution  is  likely  to  take  place 
more  rapidly  on  one  side  of  each  piece  than  on  the  other.  The  sur- 
face tension  becomes  weaker  where  the  camphor  solution  is  the 
stronger;  and  the  lump,  being  pulled  in  different  directions  by  unequal 
surface  tensions,  moves  in  the  direction  of  the  strongest  tension,  i.e., 
toward  the  side  on  which  the  least  camphor  is  dissolved.  If  a  drop 
of  ether  (a  very  volatile  liquid)  is  held  near  the  surface  of  water,  its 
vapor  will  condense  on  the  surface  of  the  water,  weakening  the 
surface  tension  there.  Surface  currents  may  be  noticed  flowing  in 
every  direction  from  under  the  drop  of  ether. 

Capillarity. 

Experiment  34.  —  Partly  fill  a'  thin,  clean  beaker  with  water,  and  a 
similar  beaker  with  clean  mercury.  Notice  that  the  upper  surfaces  of 
the  two  liquids  are  level  except  at  the  edges  near  the  glass.  Notice,  fur- 
ther, that  the  water  is  lifted  at  the  edge  by  the  glass,  and  that  the 
mercury  is  depressed. 

Experiment  35.  —  Support  a  clean  glass  rod  vertically  in  the  water, 
and  notice  that  the  liquid  is  lifted  by  the  rod,  as  shown  at  a  in 


THE   THREE   CONDITIONS   OF   MATTER. 


47 


Fig.  27.  Remove  the  rod.  Notice  that  it  is  wet.  Wipe  the  rod  dry, 
and  place  it  similarly  in  the  mercury.  Notice  that  this  liquid  is  de- 
pressed by  the  rod.  Remove  the  rod,  and  notice  that  it  was  not  wetted 
by  the  mercury. 

Smear  the  glass  rod  with  oil,  and  place  it  in  the  water,  as  before. 
Notice  that  the  water  is  depressed  thereby.  Remove  the  rod,  and 
notice  that  it  is  not  wetted  by  the  water.  Place  a  clean  strip  of  tin, 


FIG.  27. 


lead,  or  zinc,  in  the  mercury.  Notice  that  the  mercury  is  lifted. 
Remove  the  strip,  and  notice  that  the  strip  was  wetted  by  the 
mercury.  - 

47.  Capillary  Attraction.  —  The  excess  of  the  attraction 
of  one  of  two  fluids,  one  of  which  is  generally  air,  for  the 
wall  of  a  vessel  with  which  they  have  a  common  line  of 
contact,  is  called  capillary  attraction;  it  is  proximately 
accounted  for  by  surface  tension.  The  common  surface 
of  the  wall  and  of  the  more  attracted  fluid  makes  the 
acuter  angle  with  the  common  surface  of  the  fluids.  The 
truth  suggested  by  our  experiments  is  general :  all  liquids 
that  wet  the  sides  of  solids  placed  in  them  will  be  lifted^ 
while  those  that  do  not  will  be  pushed  down. 

Experiment  36.  —  So  place  two  small,  clean  glass  plates  in  a  shallow 
dish  of  clean  water,  that  the  angle  included  between  the  plates  shall 


48  SCHOOL  PHYSICS. 

be  very  acute,  and  that  the  edges  in  contact  shall  be  vertical.  The 
vertical  edges  not  in  contact  may  be  held  apart  by  a  thin  strip  of 
wood  placed  between  them,  the  whole  being  held  together  by  a  rubber 
band  placed  horizontally  around  the  plates.  Notice  the  rise  of  the 
liquid  between  the  plates,  and  the  outline  of  the  hyperbola  traced 
upon  them  by  the  surface  of  the  lifted  liquid. 

Experiment  37. —  Wet  the  inner  surfaces  of  several  clean  glass 
tubes  of  small  and  different  diameters  (1  mm.  and  less)  to  remove 
the  adhering  air-film.  Support  the  tubes  vertically  in  pure  water. 
Notice  that  the  water  rises  in  the  tubes,  as  shown  at  b  in  Fig.  27 ;  that, 
the  less  the  diameter  of  the  tube,  the  greater  the  elevation  of  the 
water ;  and  that  the  free  surface  of  the  water  in  the  tube  is  concave. 

Remove  the  tubes,  and  similarly  support  them  in  clean  mercury. 
Notice  that  the  mercury  is  depressed  in  the  tubes,  as  shown  at  c  in 
Fig.  27 ;  that,  the  less  the  diameter  of  ths  tube,  the  greater  the  depres- 
sion ;  and  that  the  free  surface  of  the  mercury  in  the  tubes  is  convex. 

Experiment  38.  —  Make  a  tapering  capillary  tube  by  drawing  out 
a  glass  tube  that  has  been  heated  to  redness.     Clean  the  tube  thor- 
oughly, and  into  its  larger  end 
introduce   a    drop   of   water. 
-       + Jiliiiii  Notice  the  concave  form  of  the 


two  free  liquid  surfaces,  and  the 
motion  of  the  water  toward 
the  smaller  end  of  the  tube. 

Empty  the  tube,  and  intro- 
FIG.  28.  duce  a  drop  of  mercury  into  the 

smaller  end.    Notice  the  convex 

form  of  the  two  free  liquid  surfaces,  and  the  motion  of  the  mercury 
toward  the  larger  end  of  the  tube. 

48.  Capillary  Tubes.  —  The  rise  of  liquids  in  capillary 
tubes  is  explained  by  the  action  of  cohesion  as  a  force  act- 
ing at  insensible  distances,  and  producing  a  tension  of  the 
superficial  film  of  the  liquid.  This  tension  produces  an 
upward  pull  where  the  liquid  surface  is  concave,  and  a 
downward  pressure  where  the  liquid  surface  is  convex. 
The  effect  of  this  tendency  is,  in  the  case  of  water,  partly 


THE  THKEE   CONDITIONS   OF   MATTER. 


49 


to  neutralize  the  downward  pull  of  gravity.     The  follow- 
ing facts  have  been  experimentally  established:  — 

(1)  Liquids  ascend  in  tubes  ivhen  they  wet  them,  i.e.,  when 
the  liquid  surface  is  concave;  and  they  are  depressed  when 
they  do  not  wet  them,  i.e.,  when  the  liquid  surface  is  convex. 

(2)  The  elevation  or  the  depression  varies  inversely  as  the 
diameter  of  the  tube. 

(3)  The  elevation  or  the  depression  decreases  as  the  tem- 
perature rises. 

(a)  The  extreme  range  of  the  forces  that  produce  capillary  action 
seems  to  lie  between  a  thousandth  and  a  twenty-thousandth  part  of  a 
millimeter.  Familiar  illustrations  of  capillary  action  are  numerous, 
such  as  the  action  of  blotting-paper,  sponges,  lamp-wicks,  etc. 

Absorption. 

Experiment  39.  —  Fill  a  large  test-tube  with  dried  ammonia  (see 
Chemistry,  §  67)  by  displacement  over  mercury.  Heat  a  piece  of 


FIG.  29. 

charcoal  to  redness,  and  plunge  it  into  the  mercury.     When  it  is  cool, 
slip  it  under  the  mouth  of  the  test-tube,  and  let  it  rise  into  the  ammonia 


50 


SCHOOL   PHYSICS. 


atmosphere.     Notice  that  the  mercury  rises  in  the  tube  as  if  the  gas 
was  absorbed  by  the  charcoal. 

49.  Absorption.  —  Some  solids  have  the  power  of  taking 
up  or  absorbing  gases.  Thus,  a  porous  body  like  charcoal 
has  the  ability  to  condense  on  its  surface  a  large  quantity 
of  some  gases  through  the  molecular  attraction  exerted 
between  its  surface  and  the  molecules  of  the  gas.  Box- 
wood charcoal  is  able  thus  to  absorb  ninety  times  its 
volume  of  ammonia  gas.  This  absorption  is  increased 
by  pressure,  and  decreased  by  a  rise  of  temperature. 


Diffusion. 

Experiment  40.  —  Half  fill  a  jar  with  water.  Through  a  long- 
stemmed  funnel  (Fig.  30)  reaching  to  the  bottom  of  the  jar,  pour  a 
strong  aqueous  solution  of  copper  sulphate 
(blue  vitriol).  The  plane  of  separation  be- 
tween the  colored  and  the  colorless  liquids  is 
clearly  visible.  Allow  the  jar  to  stand  undis- 
turbed for  several  weeks,  observing  it  from 
day  to  day.  The  plane  of  demarcation  be- 
tween the  strata  becomes  blurred,  the  liquids 
mix,  the  solution  becomes  uniform. 

Experiment  41.  —  Partly  fill  a  test-tube  or 
other  tall  glass  vessel  with  water  tinted  with 
blue  litmus.  Through  a  funnel-tube  reach- 
ing to  the  bottom  of  the  vessel,  drop  a  little 
strong  sulphuric  acid.  Notice  the  reddish 
color  (caused  by  the  action  of  the  acid  on 
:::JPIG 3Q  the  litmus)  moving  slowly  upward. 

Experiment  42.  —  Wet  the  inner  surface  of  a  clear  tumbler  or 
beaker  with  strong  ammonia  water,  leaving  a  few  drops  of  the 
liquid  in  the  bottom.  Cover  it  with  a  sheet  of  writing  paper. 
Moisten  the  inner  surface  of  a  like  vessel  with  strong  hydrochloric 
(muriatic)  acid.  Invert  the  second  vessel  over  the  first,  mouth  to 


THE   THREE   CONDITIONS  OF   MATTER. 


51 


mouth,  so  that  the  contents  of  the  two  vessels  shall  be  separated  only 

by  the  paper.     Each  vessel  is  filled  with  an  invisible  gas.     Remove 

the    paper,    and    notice 

that  the  invisible  gases 

quickly  diffuse  into  each 

other  and  form  a  dense 

cloud. 

If  two  bottles  are  filled 
with  different  gases,  as 
oxygen  and  hydrogen, 
and  the  bottles  con- 
nected'by  a  glass  tube 
two  or  three  feet  long, 
with  the  bottle  con- 
taining the  lighter  gas  FlG  31 
(hydrogen)  above  the 
other,  the  gases  still  mix  by  diffusion  through  the  tube,  but  the 

process,     of     course,     requires     more 

time. 

Experiment  43.  —  Cement  a  small 
porous  battery-cup  to  a  large  funnel- 
tube,  mouth  to  mouth.  Pass  the  end 
of  the  funnel-tube  snugly  through  the 
cork  of  a  bottle,  B,  partly  filled  with 
water,  and  provided  with  a  delivery- 
tube,  d,  drawn  out  to  a  jet,  as  shown  in 
Fig.  32.  When  a  bell-glass,  C,  contain- 
ing hydrogen  is  placed  over  the  porous 
cup,  that  gas  diffuses  inward  so  much 
more  rapidly  than  the  air  can  diffuse 
outward,  that  an  increased  pressure  is 
exerted  on  the  surface  of  the  water. 
If  all  the  joints  are  tight,  water  will  be 
thrown  from  the  jet.  The  experiment 
may  be  simplified  by  allowing  the  tube 
to  dip  into  .water  in  an  open  vessel. 
Bubbles  will  then  rise  through  the 
water. 


52  SCHOOL  PHYSICS. 

50.  Diffusion.  —  The  gradual  and  spontaneous  mixing  of 
two  fluids    that  are  placed  in  contact  is  called  diffusion. 
It  takes  place  without  application  of  external  force,  and 
even  in  opposition  to  the  force  of  gravity.    It  is  explained 
only  by  the  motions  and  attractions  of  the  molecules  of 
the  two  fluids. 

(a)  Some  liquids,  such  as  mercury  and  water,  do  not  mix  at  all 
when  placed  in  contact.  Other  liquids,  such  as  chloroform  and  water, 
mix  only  in  certain  proportions.  The  chloroform  takes  up  a  little 
water,  and  the  water  takes  up  a  little  chloroform,  but  even  the  two 
mixed  liquids  will  not  mix.  Still  other  liquids,  and  all  gases,  mix  in 
all  proportions.  When  two  such  fluids  are  placed  in  contact,  diffu- 
sion begins  of  itself,  and  goes  on  continuously  until  the  fluids  are  in 
a  state  of  uniform  mixture. 

(5)  Even  with  our  most  powerful  microscopes,  we  cannot  follow 
these  motions  or  detect  any  currents.  The  motions  are  molecular, 
not  molar. 

51.  Kinetic  Theory  of  Gases.  —  A  perfect  gas  consists 
of  free,  elastic  molecules  in  constant  and  rapid  motion. 
Each  molecule  moves  in  a  straight  line  and  with  a  uni- 
form velocity,  until  it  strikes   another   molecule  or  the 
vessel  in  which  the  gas  is  contained.     When  these  mole- 
cules encounter  each  other,  they  behave  much  as  billiard 
balls  would  do  if  no  energy  were  lost  in  their  collisions. 
Each  molecule  travels  a  very  small  distance  between  one 
encounter  and  another,  so  that  it  is  every  now  and  then 
changing  its  velocity  both  in  magnitude  and  direction. 
The  magnitude  of  the  velocity  may  be  computed,  and  one 
direction  is  just  as  likely  as  any  other. 

(a)  One  result  of  this  motion  of  free  molecules  is,  that,  if  in  any 
part  of  the  containing  vessel  the  molecules  are  more  numerous  than 
in  a  neighboring  region,  more  molecules  will  pass  from  the  first  region 
into  the  second  than  will  pass  in  the  opposite  direction ;  i.e.,  the  gas 


THE  THREE  CONDITIONS  OF  MATTER.       53 

will  diffuse  itself  equally  through  the  vessel.  Even  when  two  gases 
are  placed  in  the  same  vessel,  each  gas  diffuses  itself  in  the  same  way 
that  it  would  if  the  other  gas  was  not  present ;  but  the  molecules  of 
the  two  gases  will  encounter  each  other,  and  every  collision  will  check 
the  process.  Thus  the  interdiffusion  of  two  gases  is  slower  than  the 
equalization  of  the  density  of  a  single  gas.  It  is  said  that  in  a  given 
vessel  a  given  stage  in  the  diffusion  of  liquids  requires  as  many  days 
as  a  like  stage  in  the  diffusion  of  gases  requires  seconds. 

(6)  A  second  result  is,  that  the  blows  that  the  molecules  thus  strike 
upon  the  walls  of  the  containing  vessel  are  so  numerous,  that  their 
total  effect  is  a  continuous,  constant  force  or  pressure. 

Osmose. 

Experiment  44.  —  Tie  a  piece  of  wet  parchment-paper  over  the 
mouth  of  a  large  funnel-tube,  and  pour  a  saturated  solution  of  copper 
sulphate  into  the  stem  of  the  tube  until  the  liquid  a  little  more  than 
fills  the  bulb.  Support  the  funnel-tube  in  a  clear  glass  vessel  of  water, 
adjusting  the  height  of  the  tube  so  that  the  two  liquids  shall  stand  at 
the  same  level.  Watch  the  apparatus,  and  soon  you  may  notice  that 
the  bluish  tint  appears  in  the  water  in  the  outer  vessel,  and  that  the 
liquid  is  rising  in  the  stem  of  the  funnel-tube.  Evidently  both  liquids 
are  passing  through  the  parchment  membrane,  the  greater  flow  being 
inward. 

52.  Osmose.  —  The  tendency  of  fluids  to  pass  through 
porous  partitions  and  to  mix  is  called  osmose. 

(a)  "When  two  solutions  differing  in  strength  and  composition  are 
separated  by  a  porous  diaphragm,  they  pass  with  unequal  rapidities. 
The  action  of  the  fluid  that  passes  with  the  greater  rapidity  is  called 
endosmosis ;  that  of  the  other  fluid  is  called  exosmosis. 

(ft)  Soluble  substances  have  a  wide  range  of  diffusibility.  Bodies 
of  rapid  diffusibility  through  porous  membranes,  like  common  salt 
and  sugar,  generally  have  a  crystalline  form,  and  are  called  crystalloids. 
Bodies  of  slow  diffusibility  through  porous  membranes  generally  have 
the  amorphous,  glue-like  character  that  gives  them  the  name  of 
colloids.  Colloids  are  often  separated  from  crystalloids  by  placing 
the  mixture  in  a  vessel  having  a  parchment-paper  bottom,  and  sus- 
pending it  in  another  vessel  containing  water.  This  process  is  called 
dialysis. 


54  SCHOOL  PHYSICS. 


CLASSROOM  EXERCISES. 

1.  What  is  science  ? 

2.  What  is  matter? 

3.  Define  the  several  divisions  of  matter. 

4.  What  is  the  difference  between  a  hypothesis  and  a  theory? 

5.  (a)  What  is  a  gram?     (6)  A  liter? 

6.  On  what  property  of  matter  does  compressibility  depend? 

7.  If  you  thrust  a  knitting-needle  into  a  mass  of  dough,  is  the 
hole  thus  made  a  pore  ?    What  is  a  pore  ? 

8.  What  is  the  difference  between  a  fluid  and  a  liquid? 

9.  Are  molecules  of  water  larger  or  smaller  than  those  of  steam  ? 
Give  a  reason  for  your  answer. 

10.  Are  intermolecular  spaces  greater  in  water  or  in  steam  ?     Give 
a  reason  for  your  answer. 

11.  Considered  with  reference  to  the  three  conditions  of  matter, 
are  cohesion  and  heat  cooperative,  or  antagonistic  ? 

12.  Why  can  you  not  blow  a  soap-bubble  with  pure  water  ? 

13.  Tell  how,  with  two  pieces  of  glass  and  a  plate  of  water,  you 
can  produce  a  hyperbolic  curve. 

14.  Upon  what  property  do  most  of  the  characteristic  properties  of 
matter  depend?    Name  five  universal  and  three  characteristic  prop- 
erties of  matter.     Define  inertia. 

15.  State  definitely  how  you  could  separate  a  solution  of  loaf-sugar 
from  a  solution  of  gum-arabic  with  which  it  was  mixed.    What  is  the 
name  of  the  process  employed?    After  such  separation,  how  could  you 
separate  the  sugar  from  its  water  of  solution  ? 

16.  Find  out  how  many  pounds  you  weigh.      Express  that  weight 
in  kilograms. 

17.  State  the  kinetic  theory  of  gases. 

18.  Does  the  number  of  steps  that  a  man  takes  in  traveling  a 
mile  vary  directly  or  inversely  with  the  length  of  the  steps ;   i.e.,  does 

nccl  or  ncc- ? 

19.  If  No.  27  spring-brass  wire  breaks  under  a  load  of  15  pounds, 
calculate  the  breaking  strength  of  No.  25  brass  wire.     (See  table  of 
wire-gauge  numbers  in  the  appendix.) 

20.  If  No.  27  spring-brass  wire  has  a  breaking  strength  of  15  pounds, 
and  No.  30  annealed  iron  wire  one  of  5  pounds,  compute  the  ratio  be- 
tween the  tenacities  of  spring-brass  and  of  annealed  iron. 


THE   THREE   CONDITIONS   OF   MATTER.  55 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Draughtsman's  triangle;  proportional 
dividers ;  cardboard ;  Castile  soap ;  glycerin ;  glass  funnel ;  rubber 
tubing ;  clay  pipe ;  a  good  balance  that  weighs  to  centigrams,  and  has 
a  centigram  u  rider ;  "  a  silver  coin ;  nitric  acid ;  salt ;  ammonia  water. 

1 .  Press  one  side  of  the  triangle  firmly  against  the  edge  of  a  ruler 
resting  on  a  sheet  of  paper.     Trace  a  pencil  line  along  one  of  the 
other  sides  of  the  triangle.     Without  allowing  the  ruler  to  move, 
slide  the  triangle  along  its  edge,  and  trace  another  line  along  the  other 
edge,  as  before.     In  like  manner  draw  several  more  lines,  all  of  which 
will  be  parallel. 

2.  Draw  AB,  a  line  7.3  cm.  long.     Divide  it  into  5  equal  parts. 
From  A  draw  an  indefinite  straight  line,  AX,  making  an  angle  of  30 
or  40  degrees  with  AB.     Set  the  dividers  to  any  convenient  length, 
say  2  cm.,  and,  measuring  from  A,  lay  off  on  AX  as  many  equal 
distances  as  the  number  of  parts  into  which  AB  is  to  be  divided ;  i.e., 
5  such  equal  distances.     Mark  these  equidistant  points  on  AX,  in 
succession,  a,  b,  c,  d,  and  e.     Draw  the  straight  line  Be.     Using  the 
triangle  and  rule  as  in  Exercise  1,  draw  lines  through  d,  c,  b,  and  a, 
parallel  to  Be.     These   parallel  lines  will  divide  AB  into  5  equal 
parts,  as  required.     With  the  dividers,  test  the  equality  of  the  several 
parts  of  AB. 

3.  Divide  a  line  7  cm.  long  into  3  equal  parts.    Set  the  index  of  the 
proportional  dividers  at  the  division  on  the  scale  for  thirds.     Open 
the  dividers  until  the  points  of  the  longer  legs  rest  upon  the  ends  of 
the  given  line.     The  distance  between  the  points  of  the  shorter  legs 
may  be  laid  off  in  succession  from  one  end  of  the  given  line,  which 
will  thus  be  divided  into  thirds,  as  required. 

4.  Carefully  heat  a  tumbler,  and  half  fill  it  with  boiling  water. 
Cover  it  with    cardboard.      Invert   a   second 

tumbler  over  the  first.  Watch  the  apparatus 
for  a  few  minutes.  If  you  notice  any  change 
in  the  appearance  of  the  upper  tumbler,  find 
out  whether  it  is  due  to  a  change  in  the  inner 
or  the  outer  surface  of  the  glass.  What  prop- 
erty of  the  cardboard  is  thus  illustrated  ? 

5.  Make  of  No.  24  iron  wire  a  skeleton  of  a 
square  pyramid  with  edges   5  cm.   long,   and 

attach  a  handle,  as  shown  in  Fig.  33.    Also  make  two  wire  rings 


56  SCHOOL  PHYSICS. 

6  cm.  in  diameter  and  with  wire  handles.  Make  a  soap-bubble  solu- 
tion as  follows  :  Dissolve  10  g.  of  Castile  soap,  in  fine  shavings,  in 
400  cu.  cm.  of  warm  water,  recently  boiled,  shaking  the  mixture  from 
time  to  time.  When  the  soap  is  dissolved,  allow  the  solution  to 
stand  for  several  hours.  Pour  off  the  clear  liquid,  and  to  it  add 
250  cu.  cm.  of  good  glycerin,  shaking  the  two  thoroughly  together. 

(a)  Slip  a  piece  of  rubber  tubing  over  the  shank  of  a  glass  funnel 
about  10  cm.  across  the  top.  Dip  the  edges  of  the  funnel  into  the 
solution,  catch  a  film,  and  blow  as  large  a  bubble  as  you  can. 

(&)  Blow  a  bubble  with  a  common  clay  pipe.  Detach  it  from  the 
pipe,  and  catch  it  on  one  of  the  iron  rings.  Bring  the  other  ring  into 
contact  with  the  bubble  on  the  other  side,  and  draw  the  bubble  into 
cylindrical  form. 

(c)  Immerse  the  pyramidal  frame  into  the  solution,  and  try  to 
secure  a  film  on  each  side,  thus  forming  a  hollow,  regular  penta- 
hedron. 

6.  Weigh  accurately  a  clean  United  States  silver  coin,  which  is  an 
alloy  containing  ten  per  cent,  of  copper.  Place  two  or  three  drops  of 
strong  nitric  acid  on  the  coin,  and  allow  it  to  stand  until  the  action  of 
the  acid  on  the  coin  seems  to  cease.  Wash  the  coin  thoroughly  in  a 
tumbler  of  pure  water.  Measure  the  water  in  the  graduate  (cubic 
centimeters),  and  determine  the  number  of  drops  in  a  cubic  centi- 
meter. Divide  this  water  into  two  equal  parts.  To  one  part,  add  a  few 
drops  of  a  strong  solution  of  common  salt  (brine)  ;  the  milky  appear- 
ance indicates  the  presence  of  a  silver  compound.  To  the  other  part 
of  the  water,  add  a  few  cubic  centimeters  of  ammonia  water ;  the  blue 
tint  indicates  the  presence  of  a  copper  compound.  Weigh  the  coin 
again,  and  ascertain  how  much  of  it  was  eaten  off.  Compute  the 
weight  of  silver  and  of  copper  in  each  drop  of  the  measured  liquid. 


CHAPTER  II. 

MECHANICS:    MASS  PHYSICS. 
I.    MOTION  AND  FORCE. 

53.  Mechanics  is  the  branch   of  physics  that  treats  of 
forces  and  their  effects. 

(a)  Mechanics  is  commonly  divided  into  kinematics  and  dynamics, 
and  the  latter  into  statics  and  kinetics.  Some  of  these  distinctions 
seem  "artificial,  unscientific,  and  confused,"  and  they  will  not  be 
rigidly  observed  in  the  present  book. 

54.  Motion,    Velocity,    and    Acceleration. — Motion    is 
change  of  position.     A  body  lias  a  motion  of  translation 
when  any  point  in  it  moves  along  a  straight  line,  and  a 
motion  of  rotation  when  any  point  in  it  describes  a  circular 
arc  about  some  other  point  in  it  as  a  center.      Velocity  is 
rate  of  motion,  and  its  magnitude  is  expressed  by  say- 
ing that  it  is  such  a  distance  in  such  a  time,  as  ten  miles 
an  hour,  or  one  meter  a  second.     Velocity  may  be  uniform 
or  variable.      The  velocity  of  a  body  at  any  instant  is 
the  distance  it  would  pass  over  in  the  next  unit  of  time 
if  left  wholly  free  from  any  outside  influence.      Thus, 
the  velocity  of  a  falling  body  at  the  end  of  the  third 
second  of  its  fall  is  the  distance  it  would  pass  over  in  the 

fourth  second  if  it  could  be  freed  from  the  attraction  of 

57 


58  SCHOOL  PHYSICS. 

the  earth  and  the  resistance  of  the  air.  A  variable  velocity 
is  accelerated  or  retarded.  The  change  of  velocity  per  unit 
of  time  (i.e.,  the  rate  of  change  of  velocity)  is  called  acceler- 
ation. Acceleration  is  positive  or  negative  (+or— ) 
respectively  as  the  velocity  is  accelerated  or  retarded.  If 
the  acceleration  remains  constant,  the  velocity  is  uniformly 
accelerated  or  retarded  according  to  the  algebraic  sign  of 
the  acceleration. 

(a)  A  body  passing  over  unit  of  space  in  unit  of  time  has  unit 
velocity.  The  velocity  per  second  multiplied  by  the  number  of 
seconds  measures  the  distance  traversed  in  any  given  time  by  a  body 
moving  with  a  uniform  velocity.  Representing  these  functions  by 
I  for  distance,  v  for  velocity  per  second,  and  t  for  time  counted  in 
seconds,  we  have 

I  =  vt.  (1) 

From  this  fundamental  formula  we  derive  algebraically  the  fol- 
lowing :  — 

v  =  -,  and    t  =  -. 

t  v 

If  two  of  these  values  are  known,  they  may  be  substituted  in  one  of 
these  formulas,  and  the  third  value  obtained  thence.  If  a  body  moves 
at  the  rate  of  50  feet  per  second  for  12  seconds,  and  the  distance 
traversed  is  desired,  formula  (1)  is  applicable  :  — 

l  =  vt;  I  =  50  x  12  ;  1  =  600,  the  number  of  feet. 

(6)  Represent  constant  acceleration  by  a.  In  t  seconds,  a  body 
starting  from  rest  will  have  acquired  a  velocity  represented  by  at. 

v  =  at.  ^  (2) 

This  is  the  formula  for  a  body  starting  from  a  state  of  rest,  and  hav- 
ing a  uniformly  accelerated  velocity.  Half  the  sum  of  the  initial  and 
the  final  velocities  is  the  average  velocity.  In  the  case  now  under 
consideration,  the  initial  velocity  was  zero,  and  the  final  velocity  was 
at ;  therefore,  the  average  velocity  of  a  body  starting  from  rest,  and 

gaining  a  velocity  uniformly  accelerated  for  t  seconds,  is  — - —  or  \  at. 


MOTION  AND  FORCE.  59 

The  average  velocity  multiplied  by  the  number  of  time-units  equals 
the  distance  traversed  ;  therefore,  /  =  \  at  x  t,  or 

/  =  *<•<«.       4^v          (3> 

From  this  formula  we  derive  algebraically  the  following:  — 
a  =  *l,    and    i  =JH 


Equating  the  values  of  t  in  equations  (2)  and  (3),  we  may  deduce 
— 


the  following  : 


2a 


(c)  To  find  the  distance  passed  over  in  any  particular  unit  of  time, 
it  may  be  necessary  to  subtract  the  distance  traversed  in  t  —  1  units, 
from  the  distance  traversed  in  t  units,  the  whole  time.  Representing 
this  distance  traversed  in  a  single  time-unit  by  I',  we  have 


therefore,  /'  =  *  a(2  1  -  1).  ^^^U^^Jf5) 


(c?)  Suppose  that  a  body  moving  with  a  uniformly  accelerated 
velocity  starts  from  rest  and  passes  over  7  meters  in  the  first  second. 
How  far  does  it  move  in  the  next  3  seconds?  If  the  body  moves 
7  meters  in  the  first  second  under  the  conditions  stated,  its  average 
velocity  for  that  second  is  7  meters,  and  its  velocity  at  the  end  of 
that  time  is  14  meters.  All  of  this  velocity  is  gained  in  this  single 
second  ;  hence,  a  =  14.  Starting  from  rest,  it  moves  4  seconds-, 
hence,  t  =  4.  Substituting  these  values  in  formula  (3), 

'l  =  %at*rl  =  %  x  14  x  16  =  112, 

the  distance  passed  over  in  4  seconds.  From  this,  subtract  the  dis- 
tance passed  over  in  the  first  second,  and  we  have  105,  the  number  of 
meters  passed  over  in  the  second,  third,  and  fourth  units  of  time,  as 
called  for.  This  solution  illustrates  the  method  of  applying  physical 
formulas  to  the  solution  of  physical  problems. 

(e)  For  want  of  a  fixed  point  for  reference,  it  is  impossible  to 
determine  absolute  motion.  All  the  members  of  our  solar  system  have 
very  complicated  motions,  and  the  most  distant  stars  seem  to  have  a 
general  drift  through  space.  We  are  therefore  obliged  to  deal  exclu- 
sively with  relative  motion.  Unless  otherwise  specified,  the  motions 


60  SCHOOL  PHYSICS. 

spoken  of  in  this  book  are  relative  to  some  point  on  the  earth. 
The  point  from  which  motion  or  its  measurement  starts  is  called 
the  origin. 

55.  Laws  for  Accelerated  Motion.  —  From  the  foregoing 
we  derive  the  following  laws  for  the  motion  of  bodies 
starting  from  rest,   and  having  a  uniformly  accelerated 
velocity :  — 

(1)  The  velocity  at  the  end  of  any  unit  of  time  equals 
acceleration  multiplied  by  the  number  of  time-units.     (For- 
mula 2.) 

(2)  Acceleration  equals  twice  the  distance  traversed  in 
the  first  unit  of  time  ;  when  t  =  1,  formula  (3)  becomes 

1  =  ±a. 

(3)  The  distance   traversed  in  any  single  unit  of  time 
equals  half  the    acceleration    multiplied   by  one    less    than 
twice  the  number  of  time-units.     (Formula  5.) 

(4)  The  total  distance  traversed  in  any  given  time  equals 
half  the  acceleration  multiplied  by  the  square  of  the  number 
of  time-units.     (Formula  3.) 

56.  Graphic  Representation  of  Motions.  — A  straight  line 
may  definitely  represent  uniform  motion  in  a  straight  line, 
the  direction  of  the  line  indicating  the  direction  of  the 
motion,  and  the  length  of  the  line  representing  the  mag- 
nitude of  the  motion. 

(a)  Any  convenient  unit  of  length  may  be  chosen  to  represent  any 
unit  of  velocity,  but,  when  the  scale  has  been  determined,  it  should 
not  be  changed  in  any  given  discussion.  For  example,  two  motions, 
one  having  an  easterly  direction  and  a  magnitude  of  10  yards  per 
second,  and  the  other  having  a  southerly  direction  and  a  magnitude 
of  15  yards  per  second,  may  be  fully  represented  by  a  horizontal  line 

2  inches  long  and  a  vertical  line  3  inches  long,  the  chosen  scale  of 


MOTION  AND   FORCE.  61 

magnitudes  being  5:1;  i.e.,  each  inch  of  the  length  of  either  line 
representing  a  velocity  of  5  yards  per  second. 

(6)  In  indicating  a  line  by  the  letters  at  its  extremities,  the  order 
of  the  letters  is  that  in  which  the  line  is  to  be  drawn. 

57.-  The  Composition  of  Motions.  —  A  motion  may  be 
the  resultant  of  two  or  more  component  motions,  as 
the  motion  of  a  person  who  is  walking  on  the  deck  of  a 
moving  ship.  Under  such  conditions,  several  distinct 
cases  may  arise. 

(a)  When  two  motions  have  the  same  direction,  the  magnitude  of 
the  resultant  motion  is  the  sum  of  the  magnitudes  of  the  components, 
and  the  direction  will  be  unchanged ;  e.g.,  when  the  brakeman  on  a 
railway  freight  train  that  is  running  from  Cleveland  to  Buffalo,  at 
the  rate  of  20  miles  per  hour,  runs  at  the  rate  of  4  miles  per  hour 
along  the  car-tops  toward  the  locomotive,  he  is  really  approaching 
Buffalo  at  the  rate  of  24  miles  per  hour. 

(ft)  When  two  motions  have  opposite  directions,  the  magnitude  of 
the  resultant  motion  will  be  the  arithmetical  difference  of  the  magni- 
tudes of  the  components,  and  the  direction  will  be  that  of  the  greater 
component ;  e.g.,  when  the  brakeman  above  mentioned  runs  toward 
the  rear  of  the  train,  he  is  approaching  Buffalo  at  the  rate  of  16  miles 
per  hour. 

(c)  When  two  component  motions  have  different  directions,  the 
finding  of  the  resultant  involves  the  application  of  a  principle  known 
as  the  parallelogram  of  motions. 
The  lines  that  properly  represent 
the  components  are  made  adja- 
cent sides  of  a  parallelogram. 
The  diagonal  drawn  from  the 
angle  included  between  these 
sides  represents  the  resultant  in 
both  magnitude  and  direction. 
Thus,  let  AB  and  AC  represent 

the  two  component  motions.  Draw  BD  and  CD  to  complete  the 
parallelogram.  From  A,  the  included  angle,  draw  the  diagonal  AD. 
This  diagonal  will  be  a  complete  graphic  representation  of  the  re- 
sultant. The  resultant  will  be  greater  than  the  difference  between 


62  SCHOOL   PHYSICS. 

the  components,  and  less  than  their  sum.  If  each  component  had  a 
velocity  of  25  meters  per  second,  which  was  represented  by  lines 
25  millimeters  in  length,  and  AD  has  a  length  of  45  millimeters,  then 
the  result  of  compounding  the  two  as  indicated  will  be  motion  with  a 
velocity  of  45  meters  per  second,  and  in  the  direction  of  A  D. 

(rf)  When  the  included  angle,  as  BAC,  is  a  right  angle,  the  re- 
sultant line  is  the  hypotenuse  of  a  right-angled  triangle,  and  its 
magnitude  will  be  the  square  root  of  the  sum  of  the  squares  of  the 
components.  When  the  components  are  equal,  and  include  an  angle 
of  120  degrees,  the  resultant  divides  the  parallelogram  into  two  equi- 
lateral triangles,  and  is  equal  to  either  of  the  components.  In  other 
cases  the  magnitude  of  the  resultant  may  be  determined  by  a  careful 
construction  of  the  parallelogram  and  a  careful  measurement  of  the 
diagonal,  or,  more  accurately,  by  the  processes  of  plane  trigonometry. 

(e)  When  there  are  three  or  more  components,  the  resultant  of  any 
two  may  be  compounded  with  a.  third ;  the  resultant  thus  obtained 
may  be  compounded  with  a  fourth  component ;  etc.  The  diagonal  of 
the  last  parallelogram  thus  constructed  will  represent  the  resultant  of 
all  the  components. 

58.  The  Resolution  of  Motions. — The  converse  of  the 
process  described  in  the  last  paragraph,  i.e..  the  finding 
of  two  or  more  motions  that  may  be  substituted  as  an 
equivalent  for  a  given  motion,  is  called  the  resolution  of 
motions.     It  most  frequently  consists  in  finding  the  sides 
of  a  parallelogram  the  diagonal  of  which  represents  the 
given  motion. 

(a)  It  is  evident  that,  for  a  given  diagonal,  an  infinite  number  of 
parallelograms  may  be  constructed. 

(6)  When  the  direction  of  the  two  components  or  the  magnitude 
of  the  two  components  is  prescribed,  or  the  direction  and  the  magni- 
tude of  one  of  the  components  are  prescribed,  the  problem  becomes 
determinate. 

59.  Momentum.  —  So  far,  motion  has  been  considered, 
with  reference  to  its  speed  and  direction.     But  the  result 
of  the  action  of  a  force  upon  a  body  depends  upon  the 


MOTION  AND   FORCE.  63 

mass  of  the  body  as  well  as  upon  its  velocity.  If  m 
represents  the  mass  of  the  body,  and  v  its  velocity,  the 
product,  mv,  will  represent  its  quantity  of  motion.  This 
product  is  called  momentum. 

(a)  The  momentum  of  a  body  having  a  mass  of  20  pounds  and  a 
velocity  of  15  feet  is  twice  as  great  as  that  of  a  body  having  a  mass  of 
5  pounds  and  a  velocity  of  30  feet. 

NOTE. — The  expression  "mass  into  velocity,"  or  "mass  multiplied 
by  velocity,"  need  not  disturb  the  pupil's  ideas.  The  multiplier  must 
be  abstract,  and  the  product  must  be  of  the  same  kind  as  the  multipli- 
cand. Still,  by  a  sort  of  ellipsis,  the  abbreviated  phrase  means  the 
same  as  the  longer  one,  and  is  more  commonly  used. 

CLASSROOM  EXERCISES. 

1.  Find  the  momentum  of  a  500-pound  ball  moving  500  feet  a 
second. 

2.  By  falling  a  certain   time,  a  200-pound  ball  has   acquired  a 
velocity  of  321.6  feet.     What  is  its  momentum? 

3.  A  boat  that  is  moving  at  the  rate  of  5  miles  an  hour  weighs  4 
tons ;  another  that  is  moving  at  the  rate  of  10  miles  an  hour  weighs 
2  tons.     How  do  their  momenta  compare? 

4.  What  kind  of  motion  is  caused  by  a  single,  constant  force? 
Illustrate  your  answer. 

5.  A  stone  weighing  12  ounces  is  thrown  with  a  velocity  of  1,320 
feet  per  minute.     An  ounce  ball  is  shot  with  a  velocity  of  15  miles 
per  minute.     Find  the  ratio  between  their  momenta. 

6.  An  iceberg  of  50,000  tons  moves  with  a  velocity  of  2  miles  an 
hour.    An  avalanche  of  10,000  tons  of  snow  descends  with  a  velocity 
of  10  miles  an  hour.     Which  has  the  greater  momentum? 

7.  Two  bodies  weighing  respectively  25  and  40  pounds  have  equal 
momenta.     The  first  has  a  velocity  of  60  feet  a  second.     What  is  the 
velocity  of  the  other  ? 

8.  Two  balls  have  equal  momenta.     The  first  weighs  100  Kg.,  and 
moves  with  a  velocity  of  20  m.  a  second.     The  other  moves  with  a 
velocity  of  500  m.  a  second.     What  is  its  weight? 

9.  Three  men  start  from  Cleveland:  the  first  goes  10  miles  east- 
ward; the  second  goes  15  miles  southward;  the  third  goes  18  miles 


64  SCHOOL  PHYSICS, 

southwesterly.     Represent  these  journeys  by  lines,  using  a  scale  of 
1  inch  to  3  miles,  and  indicating  directions  by  arrowheads. 

10.  A  railway  train  moves  at  the  rate  of  40  miles  an  hour.    Express 
its  velocity  per  second  in  feet. 

11.  If  the  mean  distance  of  the  earth  from  the  sun  is  92,390,000 
miles,  and  it  requires  16  minutes  36  seconds  for  a  ray  of  light  to  pass 
over  the  diameter  of  the  earth's  orbit,  what  is  the  velocity  of  light, 
expressed  in  miles  per  second? 

12.  A  body  at  rest  receives  a  constant  acceleration  of  20  feet  per 
second.     How  far  will  it  move  in  6  seconds,  and  what  will  be  its 
velocity  at  the  end  of  that  time  ? 

13.  Draw  a  circle  and  ascertain  its  area.     (See  appendix.) 

14.  Find  the  volume  of  a  sphere  that  will  just  pass  through  the 
circle  that  you  draw. 

15.  If  the  breaking  weight  of  Xo.  27  spring-brass  wire  is  15  Ibs., 
determine  the  diameter  of  a  wire  of  the  same  material  and  quality 
that  can  just  carry  a  load  of  50  Kg. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  — A.   protractor;    a  metric  rule;   three 
balls ;  an  elastic  cord. 

1.  Draw  a  circle  3  inches  in  diameter,  and  divide  its  circumference 
into  arcs  of  10  degrees  each. 

2.  Draw  a  triangle  with  a  base  line  7.27  inches  long,  and  with 
angles  at  the  extremities  of  this  line  measuring  23  and  32  degrees 
respectively.     Measure  the   altitude   and   compute  the   area  of  the 
triangle. 

3.  Two  forces,  capable  of  giving  a  certain  body  velocities  of  35  m. 
and  of  56  m.  respectively,  act  on  that  body  at  an  angle  of  25  degrees 
with  each  other.     Determine  the  magnitude  of  the  resultant  velocity, 
and  its  direction  relative  to  that  of  the  smaller  component.     (In  your 
drawings  represent  the  direction  of  each  velocity  by  an  arrowhead.) 

4.  Resolve  a  velocity  of  50  m.  into  two  components  that  make  with 
its  direction  angles  of  20  and  45  degrees  respectively.     Use  a  scale 
of  1  :  500.     Determine  the  magnitude  of  each  component. 

5.  Resolve  a  velocity  of  20  m.  into  two  components  with  magni- 
tudes of  13  and  17  m.  respectively.     Use  a  scale  of  1  :  200.     Determine 
the  angle  that  each  component  makes  with  the  given  velocity. 

6.  Resolve  a  velocity  of  35  m.  into  two  components,  one  of  which 


MOTION  AND   FORCE.  65 

shall  have  a  magnitude  of  24.5  m.,  and  make  an  angle  of  63  degrees 
with  the  given  velocity.  Use  a  scale  of  1 : 350.  Determine  the  mag- 
nitude of  the  other  component  and  the  angle  included  between  the 
two  components. 

7.  Draw  two  lines  bisecting  each  other  at  right  angles,  and  mark 
the  ends  of  the  lines  to  represent  the  cardinal  points  of  the  compass, 
as  in  a  map.     From  the  intersection  of  the  two  lines  draw  another 
line  to  represent  the  velocity  of  a  United  States  cruiser  steaming 
south  of  southeast  at  the  rate  of  19  miles  an  hour.     Determine  the 
rate  of  the  southerly  and  the  easterly  motions  of  the  ship.     Record 
on  your  diagram  the  scale  used. 

8.  Carefully  weigh  a  meter  of  Xo.  30  copper  wire,  such  as  was  used 
in  Exercise  10,  p.  35,  and  from  the  data  ascertained  in  that  exer- 
cise calculate  the  length  of  a  piece  of  such  wire  that  would  just  break 
under  its  own  weight  when  suspended  by  one  end. 

9.  From  the  table  given  in  the  appendix,  ascertain  the  diameter 
of  Xo.  30  wire.      Calculate  the  breaking  strength  of  a  copper  rod 
1  sq.  cm.  in  cross-section,  the  quality  of  the  copper  being  the  same  as 
that  of  the  wire  used  in  Exercise  8. 

10.  On  a  level  table,  connect  two  balls  of  equal  mass  by  an  elastic 
cord  or  band.     Separate  the  balls  until  the  cord  has  been  stretched  to 
about  double  its  ordinary  length,  and  mark  the  positions  of  the  balls. 
Release  the  balls  simultaneously,  and  mark  the   place  where  they 
meet.     If  they  meet  midway  between  their  positions  as  first  marked, 
show  that  the  given  force  has  produced  equal  momenta  in  the  two 
baUs. 

11.  Repeat  Exercise  10,  using  balls  one  of  which  weighs  twice  as 
much  as  the  other.    If  one  ball  moves  twice  as  far  as  the  other,  show 
that  1  =  21';  v  =  2v' ;  mv  =  2mv'  =  mV. 

60.  Laws  of  Motion.  —  The  following  propositions, 
known  as  Newton's  Laws  of  Motion,  are  so  important, 
and  so  famous  in  the  history  of  physical  science,  that  they 
ought  to  be  remembered  by  every  student :  — 

(1)  Every  body  continues  in  its  state  of  rest  or  of  uniform 
motion  in  a  straight  line  unless  compelled  to  change  that 

state  by  an  external  force. 
5 


66  SCHOOL   PHYSICS. 

(2)  Every  change  of  motion  (momentum)  is  in  the  direc- 
tion of  the  force  impressed,  and  is  proportionate  to  it. 

(3)  Action  and  reaction  are  equal  and  opposite  in  direc- 
tion. 

61.  First  Law  of  Motion.  —  The  first  law  of  motion 
results  directly  from  inertia,  and  suggests  the  following 
definition :   Force  is  that  which  changes  or  tends  to  change 
a  body's  state  of  rest  or  motion. 

(a)  It  is  impossible  to  furnish  perfect  examples  of  this  law,  because 
all  things  within  our  reach  or  observation  are  acted  upon  by  some 
external  force. 

62.  Second  Law  of  Motion.  — The  second  law  of  motion 
is  sometimes  given  as  follows  :  A  given  force  will  produce 
the  same  effect,  whether  the  body  on  which  it  acts  is  in  motion 
or  at  rest ;  whether  it  is  acted  on  by  that  force  alone  or  by 
others  at  the  same  time.     In  the  law  as  given  by  Newton 
(§  60),  the  word  "  motion  "  is  doubtless  used  in  the  sense 
of  "momentum." 

(a)  The  law  as  given  by  Newton  points  out  that  forces  may  be 
compared  by  comparing  the  momenta  that  they  produce  in  equal 
times.  Representing  force  by  /,  mass  by  m,  and  acceleration  by  a, 
we  have/=  ma. 

If  the  forces  act  on  equal  masses,  the  changes  of  momenta  will  vary 
with  the  changes  of  velocity,  i.e.,  as  the  acceleration  ;  hence,  the 
acceleration  that  a  force  generates  may  be  used  to  measure  that  force 
(see  §  106). 

63.  Elements   of  a  Force.  —  In  treating  of  forces,  we 
have  to  consider  three  things  :  — 

(1)  The  point  of  application,  or  the  point  at  which  the 
force  acts. 


MOTION  AND  FORCE.  67 

(2)  The  direction,   or   the  right   line   along  which  it 
tends  to  move  the  point  of  application. 

(3)  The  magnitude,  or  value  when   compared  with  a 
given  standard,  or  the  relative  rate  at  winch  it  is  able 
to  produce  motion  in  a  body  free  to  move. 

64.  Measurement  of  Forces.  —  It  frequently  is  desirable 
to  compare  the  magnitudes  of  two  or  more  forces.     That 
they  may  be  compared,   they  must  be   measured;   that 
they  may  be  measured,  a  standard  of  measure  or  unit  of 
force  is  necessary.     Units  of  force  are  of  two  kinds. 

65.  The  Gravity  Unit.  —  A  force  may  be  measured  by 
comparing  it  with  the  weight  of  some  known  quantity  or 
mass  of  matter.     Although  the  force  of  gravity  varies  at 
different  placee,  this  is  a  very  simple  and  convenient  way, 
and  often  answers  every  purpose.     The  gravity  unit  of 
force  is  the  weight  of  any  standard  unit  of  mass,  as  the 
kilogram  or  pound. 

(a)  As  the  force  of  gravity  exerted  upon  a  given  mass  is  variable, 
it  will  not  suffice,  when  scientific  accuracy  is  required,  to  speak  of  a 
force  of  10  pounds,  but  we  may  speak  of  a  force  of  10  pounds  at  the 
sea-level  at  New  York  City. 

66.  The  Absolute  Unit —  The  absolute  unit  of  force  is  the 
force  that,  acting  for  unit  of  time  upon  unit  of  mass,  will 
produce  unit  of  acceleration  (i.e.,  change  of  velocity}. 

The  foot-pound-second  (F.P.S.)  unit  of  force  is  the 
force  that,  applied  to  one  pound  of  matter  for  one  second, 
will  produce  an  acceleration  of  one  foot  per  second.  It  is 
called  a  poundal. 

The  centimeter-gram-second  (C.G.S.)  unit  of  force  is 
the  force  that,  acting  for  one  second  upon  a  mass  of  one 


SCHOOL  PHYSICS. 


gram,    produces   an   acceleration   of   one   centimeter  per 
second.     It  is  called  a  dyne. 

(a)  Absolute  units  are  invariable  in  value.  Gravity  units  may 
easily  be  changed  to  absolute  units.  At  New  York  the  force  of 
gravity  acting  upon  one  pound  of  matter  left  free  to  fall 
will  produce  an  acceleration  of  32.16  feet  per  second  for 
every  second  that  it  acts;  consequently,  at  New  York  a 
force  of  one  pound  equals  32.16  poundals.  Since  the  same 
force  produces  an  acceleration  of  980  centimeters  per 
second,  it  appears  that  the  weight  of  a  gram  at  New  York 
corresponds  to  a  force  of  980  dynes. 

(6)  A  force  is  measured  in  poundals  or  dynes  by  mul- 
tiplying the  number  of  units  of  mass  moved  by  the  number 
representing  the  acceleration  produced,  only  such  units 
being  used  as  are  indicated  by  the  initials  F.P.S.  or  C.G.S. 
respectively.  The  acceleration  may  be  determined  by  di- 
viding the  total  velocity  that  the  force  has  produced  by 
the  number  of  seconds  that  the  force  has  acted. 

(c)  The  simplest  way  of  measuring  a  force  is  to  use  a 
dynamometer,  of  which  the  spring-balance  (Fig.  35)  is  a 
familiar  example.  The  dynamometer  may  be  graduated 
in  pounds,  grains,  poundals,  or  dynes. 

CLASSROOM   EXERCISES. 

1.  A  railway  train  120  yards  long  moves  at  the  rate  of  30  miles 
an  hour.     How  long  will  it  take  to  pass  completely  over  a  bridge 
120  feet  long? 

2.  At  the  sea-level  at  New  York  a  force  of  25  pounds  equals  how 
many  poundals? 

3.  Under  the  same  conditions,  a  force  of  5  Kg.  equals  how  many  dynes? 

4.  A  poundal  equals  how  many  dynes? 

5.  Compare   the   momentum  of  a  64-pound  cannon  ball  moving 
with  a  velocity  of  1,300  feet  per  second,  with  that  of  an  ounce  bullet 
moving  with  a  velocity  of  400  yards  per  second. 

6.  If  a  beam  3  m.  long,  10  cm.  wide,  and  5  cm.  thick,  is  bent  0.5  cm. 
by  a  certain  load,  how  much  would  a  similar  beam  4  in.  long  be 
depressed  by  the  same  load? 

7.  What  property  of  matter  is  illustrated  in  the  removal  of  dust 
from  a  carpet  by  beating? 


FIG.  36. 


MOTION  AND  FORCE.  69 

67.  Graphic  Representation  of  Forces.  —  Forces  may  be 
represented  by  lines,  the  point  of  application  determining 
one  end  of  the  line,  the  direction  of  the  force  determining 
the  direction  of  the  line,  and  the  magnitude  of  the  force 
determining  the  length  of  the  line. 

(a)  It  will  be  noticed  that  these  three  elements  of  a  force  (§  63) 
are  the  ones  that  define  a  line.  By  drawing  the  line  as  above 
indicated,  the  units  of  force  being  numerically  equal  to  the  units 
of  length,  we  have  a  complete  graphic  representation  of  the  given 
force.  The  unit  of  length  adopted  in  any  such  representation  may 
be  determined  by  convenience;  but, 
the  scale  once  determined,  it  must 
be  adhered  to  throughout  the  prob- 
lem. Thus,  the  diagram  represents 
two  forces  applied  at  the  point  B. 
These  forces  act  at  right  angles  to 
each  other.  The  arrowheads  indi- 


cate that  the  forces  represented  act  FIG.  36. 

from  B  toward  A  and  C  respec- 
tively. The  force  that  acts  in  the  direction,  BA,  being  20  Ibs.,  and 
the  force  acting  in  the  direction,  SC,  being  40  Ibs.,  the  line,  BA,  must 
be  one-half  as  long  as  BC.  The  scale  adopted  being  1  mm.  to  the 
pound,  the  smaller  force  will  be  represented  by  a  line  2  cm.  long, 
and  the  greater  force  by  a  line  4  cm.  long. 

68.  Resultant  Motion. — Motion  produced  by  the  joint 
action  of  two  or  more  forces  is  called  resultant  motion. 

The  single  force  that  will  produce  an  effect  like  that  of 
the  component  forces  acting  together  is  called  the  result- 
ant. The  single  force  that,  acting  with  the  component 
forces,  will  keep  the  body  at  rest  is  called  the  equilibrant. 
The  resultant  and  the  equilibrant  of  any  set  of  component 
forces  are  equal  in  magnitude,  and  opposite  in  direction. 

The  point  of  application,  direction,  and  magnitude  of 
each  of  the  component  forces  being  given,  the  direction 


70  SCHOOL  PHYSICS. 

and  magnitude  of  the  resultant  force  are  found  by  a 
method  known  as  the  composition  of  forces. 

Experiment  45.  —  Suspend  two  similar  spring-balances,  A  and  B, 
from  any  convenient  support,  as  shown  in  Fig.  37.  From  the  wooden 

rod  carried  by  their  hooks,  suspend 
a  known  weight.  Be  sure  that  the 
dynamometers  hang  vertical,  and 
therefore  parallel.  Record  the 
readings  of  the  dynamometers. 
Carefully  measure  the  distances, 
CD  and  DE,  and  record  them. 
E  If  the  dynamometers  are  accurate, 

the  work  has  been  carefully  done, 
and  the  weight  of  the  rod  is  incon- 
siderable,  the  results  should  show 
that 

W  =  A  +  B,  and  that  -  =  —  • 
B      CD 

If  the  weight  of  the  rod  is  considerable,  place  the  rod  in  the  hooks, 
and  notice  the  readings  of  the  dynamometers.  Then  hang  the  weight 
from  the  rod,  and  represent  the  increase  in  the  readings  by  A  and  B. 
The  result  should  be  as  given  above. 

69.  Composition  of  Forces.  —  Under  composition  of 
forces  there  are  several  cases,  of  which  the  more  im- 
portant are  the  following  :  — 

(1)  When  the  component  forces  act  in  the  same  direction 
and  along  the  same  line.      The  magnitude  of  the  resultant 
is  then  the  sum  of  the  given  forces.     Example  :  Rowing  a 
boat  down-stream. 

(2)  When  the  component  forces  act  in  opposite  directions 
and  along  the  same  line.     The  magnitude  of  the  resultant  is 
then  the  difference  between  the  given  forces.     Motion  will 
be  produced  in  the  direction  of  the  greater  force.     Ex- 
ample :    Rowing  a  boat  up-stream. 


MOTION  AND   FORCE.  71 

(3)  The  resultant  of  two  forces  that  act  in  the  same  direc- 
tion along  parallel  lines  has  a  magnitude  equal  to  the  sum  of 
the  magnitudes  of  the  components,  and  its  point  of  applica- 
tion divides  the  line  joining  the  points  of  application  of  the 
components  inversely  as  the  magnitudes  of  said  components. 
This  principle  is  illustrated  by  Experiment  45. 

(4)  When  two  equal  parallel  forces  act  at  different  points 
on  a  body  and  in  opposite  directions,  the  arrangement  consti- 
tutes what  is  called  a  couple.    It  produces  rotary  motion,  and 
the  components  can  have  no  resultant. 

(a)  If  a  magnetic  needle  is  placed  in  an  east  and  west  position, 
the  attraction  of  the  north  magnetic  pole  of  the  earth  attracts  one 
end  of  the  needle  and  repels  the  other  with  equal  parallel  forces,  the 
effect  of  which  is  to  turn  the  needle  upon  its  pivot  until  it  is  in  a 
north  and  south  position.  The  attraction  and  the  repulsion  constitute 
a  couple. 

(5)  When  the  component  forces  have  a  given  point  of 
application  (i.e.,  when  they  are  " concurring  forces"}  and 
act  at  an  angle  with  each  other,  as  when  a  boat  is  rowed 
across  a  stream,  the  resultant  may  be  ascertained  by  the 
"parallelogram  of  forces." 

70.   Parallelogram  of  Forces.  —  In  the  diagram,  let  AB 
and  AC  represent  two  forces 
acting  upon   the    point,    A. 
Draw  the  two  dotted  lines  to 
complete  the  parallelogram. 

From  A,  the  point  of  applica-  \  ^\\ 

tion,  draw  the  diagonal,  AD.  c  FJQ 

This  diagonal  will  be  a  com- 
plete graphic  representation  of  the  resultant.    If  two  forces, 
such  as  those  represented  in  the  diagram,  act  simultane- 


72 


SCHOOL  PHYSICS. 


ously  upon  a  body  at  A,  that  body  will  move  over  the 
path  represented  by  AD,  and  come  to  rest  at  D.  The 
process  is  very  similar  to  the  composition  of  motions 
mentioned  in  §  57. 

(a)  When  the  two  component  forces  act  at  right  angles  to  each 
other,  the  determination  of  the  numerical  value  of  the  resultant  is 
like  that  of  finding  the  length  of  the  hypotenuse  of  a  right-angled 
triangle ;  it  is  the  square  root  of  the  sum  of  the  squares  of  the  two 
components.  (See  §  57,  d.) 

Experiment  46.  —  The  principle  of  the  parallelogram  of  forces  may 
be  verified  as  follows  :  H  and  K  represent  two  pulleys  that  work  with 
very  little  friction.  Fix  them  to  the  frame  of  the  blackboard.  Knot 
together  three  silk  cords ;  pass  two  of  them  over 
the  pulleys ;  suspend  three  weights,  P,  Q,  and 
R,  as  shown  in  the  figure.  R  must  be  less  than 
the  sum  of  P  and  Q.  When  the  apparatus  has 
come  to  rest,  take  the  points,  A  and  B,  so  that 
AO  :  BO  : :  P  :  Q.  Complete  the  parallelogram, 
A  OBD,  by  drawing  lines  upon  the  board.  Draw 
the  diagonal,  OD.  It  will  be  found  by  meas- 
urement that  AO  :  OD  :  :  P  :  R  ;  or  that 
BO  :  OD  :  :  Q  :  R.  Either  equality  of  ratios 
affords  the  verification  sought. 


FIG.  3<). 


Experiment  47.  —  Modify  the  experiment  by  supporting  two  spring- 
balances,  A  and  B,  from  P  and  S,  two  nails  in  the  frame  of  the  black- 
board. Hook  them  with  a  third  dynamometer,  C,  into  a  small  ring, 
Z,  as  shown  in  Fig.  40.  Pull  steadily  on  /  in  some  downward  direc- 
tion. Mark  on  the  board  the  centers  of  the  rings,  Z  and  /,  and  record 
the  readings  of  the  three  dynamometers.  Remove  the  apparatus,  and 
through  the  points  indicated  draw  on  the  board  the  lines,  ZP,  ZS, 
and  ZI.  Using  any  convenient  scale,  lay  off  the  lines,  ZE,  ZA,  and 
ZI,  proportional  to  the  readings  of  the  respective  dynamometers. 
Complete  the  parallelogram,  ZETA.  Draw  the  diagonal,  ZT,  meas- 
ure its  length,  and  determine  the  magnitude  that  it  represents  accord- 
ing to  the  scale  adopted.  If  the  work  has  been  accurately  done, 
ZI  and  ZT  will  be  equal  in  value,  and  form  a  straight  line.  ZT 


MOTION  AND  FORCE. 


73 


is  the  resultant,  and  Zl  is  the  equilibrant,  of  the  components,  ZE 
and  ZA.     Place  the  apparatus  horizontal  and  repeat  the  work. 


FIG.  40. 

71.  Composition  of  More  than  Two  Forces.  —  If  more 
than  two  forces  concur,  the  re- 
sultant of  any  two  may  be  com- 
bined with  a  third,  their  resultant 
with  a  fourth,  and  so  on.  The 
last  diagonal  will  represent  the 
resultant  of  the  given  forces. 
As  is  indicated  by  Fig.  41,  it  is 
not  necessary  that  all  of  the  forces  act  in  the  same 
plane. 


FIG.  41. 


74  SCHOOL  PHYSICS. 

72.  Resolution  of  Forces.  —  The  operation  of  finding  the 
components  to  which  a  given  force  is  equivalent  is  called  the 
resolution  of  forces.     It  is  the  converse  of  the  composition 
of  forces.     Represent  the  given  force  by  a  line.     On  this 
line  as  a  diagonal,  construct  a  parallelogram.     An  infinite 
number  of  such  parallelograms  may  be  constructed  with 
a  given  diagonal.     Other  conditions  must  be  added  to 
make  the  problem  definite.     (See  §  58,  5.) 

(a)  By  way  of  illustration,  let  it  be  required  to  resolve  a  force  of 
20  pounds  into  two  components  that  act  at  right  angles  to  each  other, 
one  of  them  to  be  a  force  of  12  pounds.  The  problem  is  to  construct 
a  rectangle  one  side  of  which  shall  measure  12  units,  and  the  diagonal 
of  which  shall  measure  20  units.  Draw  a  vertical  and  a  horizontal 
line  intersecting  at  A.  From  A,  measure  off  12  units  on  the  vertical 
line,  thus  securing  the  point,  B.  From  B,  draw  a  line,  BX,  parallel 
to  the  horizontal  line  that  passes  through  A.  From  A  as  a  center, 
and  with  a  radius  equal  to  20  units,  describe  an  arc  cutting  BX  at 
a  point,  which  mark  C.  From  C,  draw  a  line  parallel  to  AB,  and 
intersecting  the  horizontal  line  drawn  through  A  at  a  point,  which 
mark  D.  AB  and  AD  will  be  the  components  sought. 

73.  Third  Law  of  Motion.  — Examples  of  the  third  law 
of  motion  are  very  common.     When  we  strike  an   egg 
upon  the  table,  the  reaction  of  the  table  breaks  the  egg. 
The  action  of  the  egg  may  make  a  dent  in  the  table.     The 
reaction  of  the  air,  when  struck  by  the  wings  of  a  bird, 
supports  the  bird  if  the  action  is  greater  than  the  weight. 
The  oarsman  urges  the  water  backward  with  the  same 
force  that  he  urges  his  boat  forward.    In  springing  from  a 
boat  to  the  shore,  muscular  action  tends  to  drive  the  boat 
adrift ;  the  reaction,  to  put  the  passenger  ashore.     These 
illustrations  suggest  the  idea  that  every  action  of  a  force 
develops  another  force  opposite  in  direction,  so  that  two 
forces,  instead  of  one,  are  apparently  in  action. 


MOTION  AND  FORCE. 


75 


Reaction. 

Experiment  48. — Make  a  railway  of  two  wooden  strips  1^  inches 
by  i  inch,  and  about  6  feet  long,  fastened  together  by  three  or  five 
crosspieces,  as  shown  in  Fig.  42.  The  distance  between  the  rails 
should  be  about  an  inch.  Place  the  railway  on  a  board,  and  fasten 
down  the  middle  crosspiece  with  a  screw.  Spring  up  the  ends,  and 
support  them  by  books  or  wooden  blocks.  At  the  toy  shop,  get 
several  large  glass  marbles,  or  other  elastic  balls,  and  place  them 
on  the  middle  of  the  railway.  Bring  one  ball  to  the  highest  point  of 
the  track,  and  let  it  roll  down  against  the  others.  Ball  No.  1  gives  its 
motion  to  No.  2,  and  comes  to  rest ;  No.  2  gives  it  to  No.  3,  and  in 


FIG.  42. 

turn  comes  to  rest.  The  energy  is  thus  passed  through  the  line  to 
No.  7,  which  is  driven  some  distance  on  the  up  grade,  as  to  the  posi- 
tion shown  by  the  dotted  line  at  8.  From  8,  this  ball  rolls  down 
grade,  and  passes  its  energy  along  the  line,  forcing  No.  1  up  the  grade 
to  a  lesser  distance  than  before.  The  balls  will  repeat  their  motions 
several  times,  until  they  are  finally 
brought  to  rest  by  friction,  etc. 

Experiment  49.  —  Repeat  Experi- 
ment 48  after  replacing  the  middle 
ball  by  a  lead  ball  of  the  same  size. 

Experiment  50.  —  This  action  of 
ivory  or  glass  balls  is  due  to  the  fact 
that  they  are  elastic,  and  are  flattened 
by  the  blow.  To  show  that  this  is  so, 
smear  a  flat  stone  or  iron  plate  with 
paint.  Before  the  paint  becomes  dry, 
place  one  of  the  glass  balls  on  the 
smeared  surface,  and  notice  the  size  FlG  ^ 

of  the  round  spot  thus  made.     Then 

drop  the  ball  from  a  height  of  several  inches,  and  notice  that  the 
spot  is  larger*  than  before. 


76 


SCHOOL  PHYSICS. 


74.  Elasticity  and  Reaction.  —  The  effects  of  action  and 
reaction  are  modified  largely  by  elasticity,  but  never  so  as 
to  destroy  their  equality. 

(a)  From  any  convenient  support,  as  the  door-frame,  hang,  by 
strings  of  equal  length,  two  clay  balls  of  equal  mass,  or  two  such  bags 

of  shot  or  of  sand,  so  that  they 
will  just  touch  each  other.  If 
one  is  drawn  aside  and  let  fall 
against  the  other,  both  will  move 
forward,  but  only  half  as  far  as 
the  first  would  had  it  met  no 
resistance.  The  gain  of  momen- 
tum by  the  second  is  due  to  the 
action  of  the  first.  It  is  equal  to 
the  loss  of  momentum  by  the 
first,  which  loss  is  due  to  the  re- 
action of  the  second. 

(6)  If  two  glass  or  ivory  balls, 
which  are  elastic,  are  similarly 
placed,  and  the  experiment  re- 
peated, it  will  be  found  that  the 
first  ball  will  give  the  whole  of 
its  motion  to  the  second,  and  re- 
main still  after  striking,  while 
the  second  will  swing  as  far  as 
the  first  would  have  done  if  it 
had  met  no  resistance.  In  this 
case,  as  in  the  former,  it  will  be 
seen  that  the  first  ball  loses  just  as  much  momentum  as  the  second 
gains.  These  balls  may  be  suspended  by  gluing  a  narrow  strip  of 
leather  to  each,  leaving  a  little  loop  at  the  middle  of  the  strip  for  the 
fastening  of  the  string. 

75.  Reflected  Motion  is  the  motion  produced  in  a  body  by 
the  reaction  between  it  and  another  body  against  which  it 
strikes.     A  ball  rebounding  from  the  wall  of  a  house  or 
from  the  cushion  of  a  billiard  table   is  an  example  of 
reflected  motion. 


FIG.  44. 


MOTION  AND   FORCE.  77 

76.  Law  of  Reflected  Motion. — The  angle,  ABD,  in- 
cluded between  the  direction  of  the  moving  body  before  it 
strikes  the  reflecting  surface,  and  a  perpendicular  to  that 
surface  drawn  from  the  point  of  contact,  is  called  the  angle 
of  incidence.  The  angle  between  the  perpendicular  and 
the  direction  of  the  moving  body  after  striking  is  called 
the  angle  of  reflection.  When  the  bodies  are  perfectly  elastic, 
the  angle  of  incidence  is  equal  to  the  angle  of  reflection,  and 
lies  in  the  same  plane.  When  the  elasticity  of  the  bodies  is 
imperfect,  the  angle  of  reflection  is  greater  than  the  angle  of 


incidence.  If  a  glass  or  ivory  ball  is  shot  from  A  against 
an  elastic  surface  at  B,  the  center  of  the  semicircle,  it  will 
be  reflected  back  to  O,  making  the  angles,  ABD  and  CBD, 
equal.  If  the  ball  or  the  body  at  B  is  not  perfectly  elastic 
(e.g.,  if  a  lead  ball  is  used),  the  path  of  the  ball  after  reflec- 
tion will  make  with  the  normal  line,  BD,  an  angle  greater 
than  ABD. 

77.  Curvilinear  Motion.  —  When  a  ball  at  the  end  of  a 
string  is  whirled  around  the  hand,  there  is  a  consciousness 
of  a  pull  on  the  string.  A  moment's  observation  and 
reflection  impress  one  with  the  fact  that  the  ball  is  de- 
flected by  the  tension  of  the  string  from  the  rectilinear 
path  which  it  tends  to  follow  in  accordance  with  the  first 


78  SCHOOL  PHYSICS. 

law  of  motion,  and  is  thus  constrained  to  move  in  a  curved 
line.  There  are  evidently  two  forces  involved  in  the  pro- 
duction of  such  a  motion,  —  a  tangential  component,  which 
sets  the  ball  in  motion  ;  and  a  centripetal  component,  as 
exhibited  in  the  tension  of  the  string. 

The  resistance  offered  by  the  body  to  its  deflection  from 
a  rectilinear  path  is  due  to  its  inertia,  and  is  commonly 
called  by  the  ill-chosen  name  "  centrifugal  force."  From 
this  point  of  view,  centrifugal  force  may  be  defined  as  the 
reaction  of  a  moving  body  against  the  force  that  makes  it 
move  in  a  curved  path. 

(a)  Examples  and  effects  of  this  so-called  centrifugal  force  maybe 
suggested  as  follows:  the  sling,  wagon  turning  a  corner,  railway 
curves,  water  flying  from  a  revolving  grindstone,  broken  fly-\vlieels, 
erosion  of  river-beds,  a  pail  of  water  whirled  in  a  vertical  circle,  the 
inward  leaning  of  the  circus  horse  and  rider,  the  centrifugal  drying 
apparatus  of  the  laundry  or  the  sugar  refinery,  difference  between 
polar  and  equatorial  weights  of  a  given  mass,  elongation  of  the 
equatorial  diameter  of  the  earth,  etc. 

(ft)  "  The  student  cannot  be  too  early  warned  of  the  dangerous 
error  into  which  so  many  have  fallen  who  have  supposed  that  a  mass 
has  a  tendency  to  fly  outwards  from  a  center  about  which  it  is  revolv- 
ing, and  therefore  exerts  a  centrifugal  force  which  requires  to  be 
balanced  by  a  centripetal  force."  —  Tail. 

78.  Measurement  of  Centrifugal  Forces.  —  The  laws  of 
centrifugal  force  may  be  studied  or  illustrated  by  means 
of  the  whirling  table  and  accompanying  apparatus,  some 
of  which  is  represented  in  Fig.  46.  It  may  be  shown  that 


Centrifugal  Force  = 

in  which  m  represents  the  mass  of  a  body  moving  in  a  cir- 
cular path  ;  v,  its  velocity  ;  and  r,  the  radius.  Of  course, 
the  numerical  result  will  represent  absolute  units  of  force. 


MOTION   AND   FORCE. 


79 


Tliis  formula  justifies  the  following  laws  of  centrifugal 
force :  — 

(1)  The  force  varies  directly  as  the  mass. 

(2)  The  force  varies  directly  as  the  square  of  the  velocity 
(radius  being  constant). 

(3)  The  force  varies  inversely  as  the  radius  (velocity 
being  constant). 


FIG.  46. 

CLASSROOM  EXERCISES. 

1.  Represent  graphically  the  resultant  of  two  forces,  100  and  150 
pounds  respectively,  exerted  by  two  men  pulling  a  weight  in  the  same 
direction.     Determine  its  value. 

2.  In  similar  manner,  represent  the  resultant  of  the  same  forces 
when  the  men  pull  in  opposite  directions.     Determine  its  value. 

3.  Suppose  an  attempt  is  made  to  row  a  boat  at  the  rate  of  4  miles 
an  hour  directly  across  a  stream  flowing  at  the  rate  of  3  miles  an 
hour.     Determine  the  direction  and  velocity  of  the  boat. 

4.  A  flag  is  drawn  steadily  downward  64  feet  from  the  masthead  of 
a  moving  ship.     During  the  same  time,  the  ship  moves  forward  24:  feet. 
Represent  the  direction  and  length  of  the  actual  path  of  the  flag. 

5.  A  sailor  climbs  a  mast  at  the  rate  of  3  feet  a  second.    The  ship  is 
sailing  at  the  rate  of  12  feet  a  second.     Over  what  space  does  he 
actually  move  during  20  seconds? 

6.  A  foot-ball  simultaneously  receives  three  horizontal  blows,  —  one 
from  the  north,  having  a  force  of  10  pounds ;  one  from  the  east,  having 


80  SCHOOL  PHYSICS. 

a  force  of  15  pounds ;  and  one  from  the  southeast,  having  a  force  of 
25  pounds.     Determine  the  direction  of  its  motion. 

7.  Why  does  a  cannon  recoil  or  a  shot-gun  "kick"  when  fired? 
Why  does  not  the  velocity  of  the  gun  equal  the  velocity  of  the 
ball? 

8.  If  the  river  mentioned  in  Exercise  3  is  a  mile  wide,  how  far 
did  the  boat  move,  and  how  much  longer  did  it  take  to  cross  than  if 
the  water  had  been  still  ? 

9.  A  plank  12  feet  long  has  one  end  on  the  floor,  and  the  other  end 
raised  6  feet.     A  50-pound  cask  is  being  rolled  up  the  plank.     Resolve 
the  gravity  of  the  cask  into  two  components,  —  one  perpendicular  to 
the  plank,  to  indicate  the  plank's  upward  pressure ;  and  one  parallel 
to  the  plank,  to  indicate  the  muscular  force  needed  to  hold  the  cask  in 
place.     Find  the  magnitude  of  this  needed  muscular  force. 

10.  To  how  many  poundals  is  a  force  of  60  pounds  equal  ? 

11.  To  how  many  dynes  is  a  force  of  60  kilograms  equal? 

12.  What  is  meant  by  a  force  of  10  pounds?     To  how  many 
poundals  is  it  equal  ? 

13.  A  force  of  1,000  dynes  acts  on  a  certain  mass  for  one  second,  and 
gives  it  a  velocity  of  20  cm.  per  second.     What  is  the  mass  in  grams  ? 

Ans.  50. 

14.  A  constant  force,  acting  on  a  mass  of  12  g.  for  one  second,  gives 
it  a  velocity  of  6  cm.  per  second.    Find  the  force  in  dynes. 

15. -A  force  of  490  dynes  acts  on  a  mass  of  70  g.  for  one  second. 
What  velocity  will  be  produced?  Ans.  7  cm.  per  second. 

16.  Show  how  the  principle  of  resolution  of  forces  and  the  prin- 
ciple  of  the  'couple   may  be   applied   to   explain   the   action   of    a 
windmill. 

17.  Determine,  in  absolute   units,  the  centrifugal  force  of  a  10- 
pound  body  moving  with  a  velocity  of  20  feet  per  second,  in  a  circle 
of  5  feet  radius.  Ans.  800  poundals. 

18.  Without  drawing  a  diagram,  find  the  numerical  value  of  the 
resultant  of  two  concurrent  forces  of  5  Kg.  and  12  Kg.  respectively, 
acting  at  right  angles  to  each  other. 

19.  Resolve  a  force  of  30  pounds  into  two  component  forces  acting 
at  a  right  angle,  one  of  them  being  a  force  of  18  pounds. 

20.  Determine  the  point  of  application  of  the  resultant  of  two 
forces  of  8  and  11  pounds  respectively,  acting  in  the  same  direction 
along  parallel  lines  57  inches  apart. 

21.  A  railway  train  is  moving  southeastward  at  the  rate  of  30  miles 


MOTION   AND   FORCE.  81 

an  hour,     (a)  How  fast  is  it  moving  eastward?     (&)  How  fast  is  it 
moving  southward? 

22.  A  mass  of  10  Kg.  moves  with  a  velocity  of  20  m.  a  second  in  a 
circular  path  with  a  radius  of  10  m.     What  is  its  centrifugal  force? 

23.  (a)  What  will  be  the  effect  upon  the  motion  of  a  boat  if  air 
is  blown  directly  against  the  sail  from  a  huge  bellows  placed  astern  ? 
(6)  What  will  be  the  effect  if  the  air  is  drawn  in  by  a  valve  under 
the  bellows,  and  forced  out  directly  backward  ? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc. — Two  small  pulleys  that  work  with  very 
little  friction;  two  good  spring-balances;  a  fish-line  or  other  stout, 
flexible  cord ;  a  sheet  of  paper ;  four  thumb-tacks ;  boards ;  hammer 
and  nails ;  brace  and  bits  ;  hand-saw. 

1.  Bore  a  small  hole  through  a  meter  stick  at  the  middle  of  its 
length  and  near  one  edge.  Through  this  hole,  pass  a  wire  nail  of 
such  size  that  it  may  carry  a  good  load  and  yet  allow  the  stick  to 
turn  freely  upon  it  as  an  axis.  Make  a  stout  wire  clevis  that  shall 
come  down  on  each  side  of  the  stick  and  support  each  end  of  the  nail 
without  rubbing  the  sides  of  the  stick.  Through  the  upper  part  of 
the  clevis,  pass  the  hook  of  a  spring-balance,  and  support  the  dyna- 
mometer so  that  the  stick  may  hang  at  an  elevation  convenient  for  ob- 
servation. As  the  stick  hangs  in  the  clevis  with  the  hole  near  its  upper 
edge,  load  one  end  of  it  with  putty  until  the  stick  hangs  horizontal. 
Note  the  reading  of  the  dynamometer.  Over  each  end  of  the  stick, 
slip  a  loose  single  loop  of  silk  thread,  the  weight  of  which  may  be 
ignored;  from  them  hang  unequal  but  known  weights.  Shift  the 
position  of  the  weights  until  the  loaded  apparatus  hangs  in  equilib- 
rium. Note  the  distance  of  each  loop  from  the  middle  of  the  stick, 
and  the  reading  of  the  dynamometer.  Determine  the  ratio  between 
the  sum  of  the  two  suspended  weights  and  the  difference  between  the 
two  observed  readings  of  the  dynamometer.  Using  the  scale  of  1  to 
10,  draw  a  horizontal  line  to  represent  the  meter  stick,  and  mark  its 
middle  point  F.  On  this  line,  represent  the  points  of  application  of 
the  two  suspended  weights,  and  mark  them  P  and  W.  Using  any 
convenient  scale,  draw  lines  from  P  and  W,  and  place  arrowheads  to 
represent  the  forces  acting  at  those  points.  In  similar  manner,  draw 
and  mark  a  line  to  represent  the  equilibrant  of  those  forces.  Add  a 
reference  to  the  paragraph  of  this  book  that  treats  of  the  subject 
chiefly  illustrated  by  this  exercise. 
6 


82  SCHOOL  PHYSICS. 

2.  Two  forces  pulling  toward  the  east  act  on  two  points  of  a  rigid 
body  5  feet  asunder.     Represent  this  body  by  a  vertical  line,  on 
which  locate  the  two  points  of  application,  using  the  scale  of  an  inch 
to  the  foot.     One  of  these  forces  has  a  magnitude  of  7  pounds,  and  the 
other  has  one  of  11  pounds.     Using  the  scale  of  a  half-inch  to  the 
pound,  draw  graphic  representations  of  these  forces,  their  resultant 
and  their  equilibrant. 

3.  Arrange  apparatus  as  shown  in  Fig.  39.    Make  P  equal  5  pounds, 
and  Q  equal  7  pounds.     Add  unknown  weights  at  li  until  the  cords, 
OH  and  OK,  include  an  angle  that  is  acute  or  not  very  obtuse.     Back 
of  the  cords  around  0,  support  a  board  of  such  thickness  that  the 
face  of  the  board  shall  j  ust  touch  the  cords.     With  thumb-tacks,  fasten 
a  sheet  of  paper  to  this  board  ;  and  on  the  paper,  with  rule  and  pencil, 
draw  lines  from  0  in  the  direction  of  H,  K,  and  R.    Using  the  scale 
of  a  half-inch  to  the  pound,  represent  forces  acting  from  0  along  the 
lines,  OH  and  OK,  with  magnitudes  of  5  and  7  pounds  respectively. 
Complete  the  parallelogram,  and  draw  the  diagonal,  OD.    Lay  off  from 
0,  and  on  the  line,  OR,  a  distance  equal  to  OD.    Which  line  on  your 
paper  represents  the  gravity  of  the  unknown  weight?    From  the 
length  of  this  line  compute  the  mass  of  R.    Place  R  on  the  balance 
or  hang  it  from  the  spring-balance,  and  thus  determine  its  mass  by 
weighing.     Compare  these  two  results.     Does  OD  form  a  continua- 
tion of  the  straight  line,  ROf    If  it  does  not,  your  work  has  been  ill 
done.     If  ROD  is  a  straight  line,  what  does  OD  represent? 

4.  Provide  two  strings,  each  about  a  foot  long.     Tie  one  end  of 
one  string  to  the  ring  of  a  spring-balance.     Tie  one  end  of  the  other 
string  to  the  ring  of  another  spring-balance.    By  these  strings,  sup- 
port the  dynamometers  from  nails  driven  at  points  about  one  corner 
of  the  blackboard,  and  corresponding  more  or  less  closely  to  H  and  K 
in  Fig.  39.      Cut  off  two  pieces  of  cord,  each  about  2  feet  long. 
Tie  a  small  loop  that  will  not  slip  at  each  end  of  each  cord.    Pass  the 
first  cord  through  the  loop  at  one  end  of  the  second  cord.     Pass  the 
loops  at  the  ends  of  the  first  cord  over  the  hooks  of  the  two  dyna- 
mometers.    To  the  free  end  of  the  second  cord,  attach  a  weight  of 
10  pounds.     The  loop  at  the  upper  end  of  the  cord  that  carries  the 
weight  will  slip  along  the  length  of  the  cord  that  joins  the  dyna- 
mometers until  the  apparatus  is  in  equilibrium.    Place  the  board  carry- 
ing a  fresh  sheet  of  paper  as  was  done  in  the  last  exercise.     On  the 
paper,  mark  three  intersecting  lines  as  indicated  by  the  strings  between 
the  dynamometers  and  the  load,  and  mark  their  common  point  of 


WORK   AND   ENERGY.  83 

intersection  2T,  as  in  Fig.  40.  Prolong  the  vertical  line  upward  5 
inches  to  a  point,  which  mark  T.  Construct  the  parallelogram  of 
which  ZT  is  a  diagonal,  and  the  two  sides  of  which,  meeting  at  Z, 
coincide  with  the  lines  already  drawn  upon  the  paper.  Mark  the 
left-hand  corner  of  the  parallelogram  E,  and  the  opposite  corner 
A .  What  does  Z  T  represent  ?  What  is  the  scale  adopted  ?  On  that 
scale  determine  the  magnitudes  represented  by  the  lengths  of  ZE 
and  ZA.  Compare  these  magnitudes  with  the  readings  of  the 
dynamometers,  and  determine  the  magnitude  of  the  error  of  your 
work.  Record  a  reference  to  the  paragraph  in  the  text-book  illus- 
trated and  approximately  verified  by  this  exercise. 

5.  Change  the  point  of  support  of  one  of  the  dynamometers  so  as 
to  increase  the  angle  included  between  the  component  forces.     Repeat 
the  experiment. 

6.  Change  the  point  of  support  of  one  of  the  dynamometers  so  as 
to  make  the  angle  between  the  components  very  acute.     Repeat  the 
experiment.     Compare  the  diagram  made  with  those  made  in  Exer- 
cises 4  and  5. 

7.  Without  using  a  protractor,  lay  off  an  angle  of  60°. 

8.  Two  forces,  of  7  and  16  units  respectively,  have  a  resultant  of 
21  units.     By  construction  and  measurement,  determine  the  angle 
between  the  two  components. 


II.    WORK  AND  ENERGY. 

79.  Work.  —  In  physical  science,  the  word  "work" 
signifies  the  overcoming  of  resistance  of  any  kind.  Work 
implies  a  change  of  position,  and  is  independent  of  the 
time  taken  to  do  it.  When  a  force  causes  motion  through 
space,  i.e.,  when  it  moves  a  body,  it  is  said  to  do  work  on 
that  body.  When  the  expansive  force  of  steam  presses 
against  the  piston  of  an  engine  and  overcomes  the  resist- 
ance, i.e.,  when  it  moves  the  piston,  it  does  work. 

(a)  A  man  who  is  supporting  (not  lifting)  a  heavy  weight  may  be 
putting  forth  great  effort,  but  he  is  not  doing  work  in  the  scientific 
sense  of  that  expression. 


84  SCHOOL  PHYSICS. 

80.  Units  of  Work.  —  It  is  often  necessary  to  represent 
work  numerically ;  hence  the  necessity  for  a  unit  of  meas- 
urement. Four  work-units  are  in  use  ;  viz.,  the  foot-pound 
and  the  kilogrammeter  (which  are  gravitation  units),  and 
the  foot-poundal  and  the  erg  (which  are  absolute  units). 

(1)  The  foot-pound  is  the  amount  of  work  required  to 
raise  one  pound  one  foot  high  against  the  force  of  gravity. 
It   is   the   unit  in  common  use  among  English-speaking 
engineers.     See  Appendix  1. 

(2)  The  kilogrammeter  is  the  amount  of  work  required  to 
raise  one  kilogram  one  meter  high  against  the  force  of  gravity. 

(3)  The  foot-poundal  is  the  amount  of  work  done  by  a 
force  of  one  poundal  in  producing  a  displacement  of  one  foot. 
It  is  numerically  equal  to  the  foot-pound  multiplied  by 
the  acceleration  of  gravity  expressed  in  feet  per  second ; 
thus,  at  New  York,  a  foot-pound  is  equivalent  to  32.16 
foot-poundals. 

(4)  The  erg  is  the  amount  of  work  done  by  a  force  of  one 
dyne  producing  a  displacement  of  one  centimeter.     It  is  the 
unit  in  common  use  among  scientists.     Since  there  are 
980,000  dynes  in  the  weight  of  one  kilogram  of  matter  at 
New  York,  a  kilogrammeter  there  equals  98,000,000  ergs. 
A  foot-poundal  is  equivalent  to  421,402  ergs ;  a  foot-pound 
is  equivalent  to  32.16  times  that  many  ergs. 

(a)  To  get  a  numerical  estimate  of  work  done,  we  multiply  the 
number  of  units  of  force  by  the  number  of  units  of  displacement : 

Work  done  =fi. 

Since  the  resistance  overcome  is  numerically  equal  to  the  force  acting, 
the  work  done  may  be  computed  by  multiplying,  in  a  similar  manner, 
the  resistance  by  the  space  : 

Work  done  —  wl. 


WORK  AND   ENERGY.  85 

In  this  formula,  w  represents  the  resistance ;  and  Z,  the  length  or  dis- 
tance. When  the  body  is  simply  lifted  against  the  force  of  gravity, 
w  represents  weight.  A  weight  of  25  pounds  raised  3  feet,  or  one 
of  3  pounds  raised  25  feet,  represents  75  foot-pounds.  A  weight  of 
15  kilograms  raised  10  meters  represents  150  kilogram  meters. 

81.  Activity  and   Horse-Power.  —  In  measuring   work 
done,  no  consideration  is  given  to  the  time  taken.     In 
considering  an  engine  or  other  agent  that  is  to  do  the 
work,  the  time  required  is  a  very  important  thing.      The 
activity  of  an  agent  is  the  rate  at  which  it  can  do  work,  and 
is  measured  by  the  work  it  can  do  in  unit  time.     The  unit  in 
most  common  use  for  the  measurement  of  activity  is  the  horse- 
power.    It  represents  the  ability  to  do  550  foot-pounds  per 
second. 

TT  p  _  pounds  x  feet 
~~  550  x  seconds' 

(a)  The  practical  unit  of  electrical  activity  is  the  watt,  which  is^ 
equal  to  107  ergs  per  second.  One  horse-power  equals  746  watts,  or 
746  x  107  ergs  per  second. 

82.  Energy  is  the  power  of  doing  work,  and  is  possessed 
by  bodies  by  virtue  of  work  having  been  done  upon  them. 
If  a  falling  cannon  ball  can  overcome  a  greater  resistance 
than  a  flying  base-ball,  it  has  more  energy ;  more  work 
was  done  upon  it. 

The  two  fundamental  ideas  with  which  physics  concerns 
itself  are  matter  and  energy. 

(a)  "  We  are  acquainted  with  matter  only  as  that  which  may  have 
energy  communicated  to  it  from  other  matter.  Energy,  on  the  other 
hand,  we  know  only  as  that  which,  in  all  natural  phenomena,  is  con- 
tinually passing  from  one  portion  of  matter  to  another.  It  cannot 
exist,  except  in  connection  with  matter."  —  Maxwell. 


86  SCHOOL  PHYSICS. 

83.  Types  of  Energy.  —  It  is  a  general  and  familiar  fact 
that  bodies  in  motion  can  do  work  on  other  bodies.  A 
camion  ball  falling  toward  the  earth  has  energy,  because 
of  its  mass  and  its  velocity.  Even  before  it  began  to  fall, 
it  had  a  power  of  doing  work,  because  work  had  been  done 
in  lifting  it  into  its  elevated  position.  Thus  there  are 
two  types  of  energy,  which  may  be  designated  as  energy 
of  motion  and  energy  of  position.  Energy  of  motion  is 
called  kinetic  energy  ;  energy  of  position  is  called  potential 
energy.  Energy  that  is  not  kinetic  is  potential. 

(a)  A  falling  weight  or  running  stream  possesses  energy  of  motion  ; 
it  is  able  to  overcome  resistance  by  reason  of  its  mass  and  velocity. 
On  the  other  hand,  before  the  weight  began  to  fall,  it  had  the  power 
of  doing  work  by  reason  of  its  elevated  position  with  reference  to  the 
earth.  When  the  water  of  the  running  stream  was  at  rest  in  the  lake 
among  the  hills,  it  had  a  power  of  doing  work,  an  energy  that  was 
not  possessed  by  the  waters  of  the  pond  in  the  valley  below.  In 
either  case,  work  had  to  be  done  to  lift  the  body  into  its  elevated 
position,  and  thus  to  endow  it  with  potential  energy.  In  bending  a 
bow,  or  in  elongating  the  spring  of  a  dynamometer,  or  in  winding  up 
a  watch,  work  is  performed  in  distorting  the  bow  or  the  spring,  and, 
by  virtue  of  this  distortion,  the  instruments  possess  potential  energy. 

(6)  Kinetic  and  potential  energies  are  interconvertible.  Imagine 
a  ball  thrown  upward  with  a  velocity  that  will  keep  it  in  motion  for 
two  seconds.  At  the  end  of  one  second  it  has  lost  some  of  its  initial 
velocity,  and  hence  some  of  its  kinetic  energy ;  but  it  has  gained  an 
elevated  position,  and  has  therefore  acquired  some  potential  energy. 
This  -potential  energy  just  equals  the  loss  of  kinetic  energy,  and  exists 
by  virtue  of  that  loss.  At  the  end  of  another  second  it  has  no  ve- 
locity, and,  therefore,  no  kinetic  energy.  But  the  energy  with  which 
the  ball  began  its  upward  flight  has  not  been  annihilated ;  it  has  been 
wholly  converted  into  potential  energy.  If  at  this  moment  the  ball 
is  caught,  all  of  the  original  kinetic  energy  may  be  kept  in  store  as 
potential  energy. 

(c)  If  we  ignore  the  disappearance  (not  loss)  of  the  energy 
expended  in  overcoming  the  resistance  of  the  air,  the  ball  would, 
when  permitted  to  fall,  reach  the  level  from  which  it  started  with  its 


WORK   AND   ENERGY. 


87 


original  velocity  and  kinetic  energy.  At  the  start,  at  the  finish,  or  at 
any  intermediate  point  of  either  its  ascent  or  descent,  the  sum  of  the 
two  types  of  energy  is  the  same.  It  may  be  all  kinetic,  all  potential, 
or  partly  both,  but  the  sum  of  the  two  is  constant. 

(rf)  The  pendulum  affords  a  good  and  simple  illustration  of  kinetic 
and  potential  energy,  their  equivalence  and  convertibility.  When  the 
pendulum  hangs  at  rest  in  a  vertical  position,  as  Pa,  it  has  no  energy 
at  all.  Considered  as  a  mass  of  mat- 
ter separated  from  the  earth,  it  cer- 
tainly has  potential  energy;  but 
considered  as  a  pendulum,  it  has  not. 
If  we  draw  the  pendulum  aside  to  b, 
we  raise  it  through  the  space,  ah; 
that  is,  we  do  work  upon  it.  The 
energy  thus  expended  is  now  stored 
up  as  potential  energy,  ready  to  be 
reconverted  into  energy  of  the  kinetic 
type,  whenever  we  let  it  drop.  As  it 
falls  the  distance,  Aa,  in  passing  from 
b  to  a,  this  reconversion  is  gradually 
going  on.  When  the  pendulum 
reaches  a,  its  energy  is  all  kinetic,  and  just  equal  to  that  spent  in 
raising  it  from  a  to  b.  This  kinetic  energy  now  carries  it  on  to  c, 
lifting  it  again  through-  the  space,  ah.  Its  energy  is  again  all  poten- 
tial, just  as  it  was  at  b.  If  we  could  free  the  pendulum  from  the 
resistances  of  the  air  and  friction,  the  energy  originally  imparted  to 
it  would  swing  to  and  fro  between  the  extremes  of  all  potential  and 
all  kinetic;  but,  at  every  instant,  and  at  every  point  of  the  arc 
traversed,  the  total  energy  would  be  an  unvarying  quantity,  always 
equal  to  the  energy  originally  exerted  in  swinging  it  from  a  to  b. 

Velocity  and  Energy. 

Experiment  51.  —  Into  a  pail  full  of  moist  clay  or  stiff  mortar,  drop 
a  bullet  from  the  height  of  one  yard.  Xotice  the  depth  to  which  the 
bullet  penetrates.  Drop  the  bullet  from  a  height  of  four  yards.  It 
will  strike  fche  clay  with  twice  the  velocity  (§  107)  and  penetrate 
four  times  as  far  as  it  did  before.  This  suggests  that  perhaps  an 
increase  in  the  velocity  of  a  given  body  increases  the  energy  of  that 
body  more  rapidly  than  it  increases  the  momentum;  that  the  mass 
being  the  same,  the  energy  varies  as  the.  square  of  the  velocity ;  E  cc  v2. 


88  SCHOOL  PHYSICS. 

84.  Relation    of    Velocity  to  Energy. — Any    moving 
body  can  overcome  resistance,  or  perform  work  ;  it  has 
energy.     We   must   acquire  the  ability  to  measure   this 
energy.     In  the  first  place,  we  may  notice  that  its  defi- 
nition indicates  that  it  may  be  measured  by  the  units  used 
in  measuring  work;  i.e.,  in  units  of  force  and  displacement. 
In  the  next  place,  we  may  notice  that  the  direction  of  the 
motion  is  unimportant.     A   body  of  given  weight   and 
velocity  can  at  any  instant  do  as  much  work  when  going 
in  one  direction  as  when  going  in  another.     This  energy 
may  be  expended  in  penetrating  an  earth-bank,  knocking 
down  a  wall,  or  lifting  itself  against  the  force  of  gravity. 
Whatever  the  work  actually  done,  the  manner  of  expend- 
iture does  not  change  the  amount  of  energy  expended. 
We  may  therefore  find  to   what  vertical  height  the  given 
velocity  would  lift  the  body  (§  110),  and  thus  determine 
its  energy  in  foot-pounds  or  kilogr  ammeters. 

85.  Kinetic  Energy  Measured  in  Gravitation  Units. — 
Representing  the  weight  of  a  body  by  w,  and  the  vertical 
height  to  which  its  velocity  can  carry  it  by  Z,  it  is  evident 
that   the   kinetic   energy   can   do   wxl  units   of   work. 
When  we  come  to  study  the  laws  of  falling  bodies,  we 
shall  find  that 

l=W 

in  which  g  represents  the  acceleration  due  to  gravity,  i.e., 
32.16  feet  or  980  cm.  (see  §107,  c?).  Substituting  this 
value  of  I  in  the  equation  given  above,  we  have 

2 

Kinetic  Energy  =  — — . 


WORK   AND   ENERGY.  89 

If  w  is  measured  in  pounds  and  v  in  feet,  this  measures 
the  energy  in  foot-pounds  ;  if  w  is  measured  in  kilograms 
and  v  in  meters,  it  measures  the  energy  in  kilogram- 
meters. 

(a)  In  measuring  work,  we  consider  resistance  and  the  distance 
through  which  it  is  overcome  ;  in  measuring  energy,  we  consider  the 
force  and  the  distance  through  which  it  acts.  A  foot-pound  of  energy 
is  the  amount  of  energy  that  must  be  expended  in  doing,  or  that  is 
capable  of  doing,  a  foot-pound  of  work.  Similarly,  a  kilogrammeter 
of  energy  is  the  amount  of  energy  that  must  be  expended  in  doing,  or 
that  is  capable  of  doing,  a  kilogrammeter  of  work. 

86.  Kinetic  Energy  Measured  in  Absolute  Units.  —  We 
have  already  seen  (§  62,  a)  that  a  force  may  be  measured 
by  the  momentum  it  produces. 

/=  ma- 

But  the  measurement  of  work  (§  80,  a)  introduces  the 
additional  factor,  ?,  representing  the  number  of  units  of 
displacement.  Introducing  this  factor  into  the  equation 
above,  we  have,  for  work  or  kinetic  energy, 

K.E.  =fl  =  mal 
In  §  54  (6)  we  have 

'*=#'• 

2a 

Substituting  this  value  of  I  in  the  second  member  of  the 
equation  above,  we  have 


(a)  If  m  is  measured  in  pounds  and  v  in  feet,  this  formula  gives 
a  numerical  expression  for  foot-poundals  ;  if  m  is  measured  in  grams 
and  v  in  centimeters,  it  gives  that  expression  in  ergs.  Foot-poundals 
may  be  reduced  to  foot-pounds  by  dividing  by  32.16,  the  value  of  g; 
ergs  may  be  reduced  to  kilogrammeters  by  dividing  by  98,000,000. 


90  SCHOOL  PHYSICS. 

87.  Potential  Energy  Measured.  —  In  the  case  of  a  body 
raised  above  the  surface  of  the  earth,  its  potential  energy 
may  be   measured, 

(1)  In  gravitation  units,  by  the  product  w  x  h. 

(2)  In  absolute  units,  by  the  product  m  x  h  x  g. 

88.  Conservation  of  Energy.  —  In  §  83  (d)  it  was  stated 
that,  were  it  not  for  friction  and  the  resistance  of  the 
air,  the  pendulum  would  vibrate  forever  ;   that  the  energy 
would  be  indestructible.     Energy  is  withdrawn  from  the 
pendulum  to  overcome  these  impediments,  but  the  energy 
thus  withdrawn  is  not  destroyed.     What  becomes  of  it 
will  be  seen  when  we  study  heat.     The  truth  is  that  en- 
ergy is  as  indestructible  as  matter;  this  is  what  is  meant  by 
the  conservation  of  energy. 

(a}  Energy  cannot  be  created ;  it  cannot  be  destroyed.  Taking 
the  universe  as  a  whole,  its  quantity  is  unchangeable.  For  the  present 
we  must  admit  that  a  given  amount  of  energy  may  disappear,  and 
escape  our  search,  but  it  is  only  for  the  present.  We  shall  soon  learn 
to  recognize  the  fugitive  even  in  disguise. 

(/;)  Transformations  of  energy  are  constantly  recurring,  and  it  is 
the  prime  duty  of  every  student  of  physical  science  to  watch  for  them 
and  to  try  to  recognize  them  in  every  phenomenon. 

CLASSROOM  EXERCISES. 

1.  What  is  the  horse-power  of  an  engine  that  will  raise  8,250  pounds 
176  feet  in  4  minutes  ? 

2.  A  ball  weighing  192.96  pounds  is  rolled  with  a  velocity  of  100 
feet  a  second.     How  much  energy  has  it  ?       A  ns.  30,000  foot-pounds. 

3.  A  projectile  weighing  50  Kg.  is  thrown  obliquely  upward  with 
a  velocity  of  19.6  m.     How  much  kinetic  energy  has  it? 

4.  Two  bodies  weigh  50  pounds  and  75  pounds  respectively,  and 
have  equal  momenta.     The  first  has  a  velocity  of  750  feet  per  second. 
What  is  the  velocity  of  the  second  ? 

5.  A  body  weighing  40  Kg.  moves  at  the  rate  of  30  Km.  per  hour, 
Find  its  kinetic  energy. 


WORK  AND  ENERGY.  91 

6.  What  is  the  horse-power  of  an  engine  that  can  raise  1,500 
pounds  2,376  feet  in  3  minutes?  Ans.  36  H.P. 

7.  A  cubic  foot  of  water  weighs  about  62  \  pounds.     What  is  the 
horse-power  of  an  engine  that  can  raise  300  cubic  feet  of  water  every 
minute  from  a  mine  132  feet  deep. 

8.  A  body  weighing  100  pounds  moves  with  a  velocity  of  20  miles 
per  hour.     Find  its  kinetic  energy. 

9.  A  weight  of  3  tons  is  lifted  50  feet,     (a)  How  much  work  was 
done  by  the  agent  ?    (6)  If  the  work  was  done  in  a  half  minute,  what 
was  the  necessary  horse-power  of  the  agent  ? 

10.  How  long  will  it  take  a  2-horse-power  engine  to  raise  5  tons 
100  feet? 

11.  How  far  can  a  2-horse-power  engine  raise  5  tons  in  30  seconds? 

12.  What  is  the  horse-power  of  an  engine  that  can  do  1,650,000 
foot-pounds  of  work  in  a  minute  ? 

13.  What  is  the  horse-power  of  an  engine  that  can  raise  2,376 
pounds  1,000  feet  in  2  minutes? 

14.  If  a  perfect  sphere  rests  on  a  perfect  horizontal  plane  in  a 
vacuum,  there  will  be  no  resistance,  other  than  its  own  inertia,  to 
a  force  tending  to  move  it.     How  much  work  is  necessary  to  give 
to  such  a  sphere,  under  such  circumstances,  a  velocity  of  20  feet  a 
second,  if  the  sphere  weighs  201  pounds?         Ans.  1,250  foot-pounds. 

15.  A  railway  car  weighs  10  tons.     From  a  state  of  rest  it  is  moved 
50  feet,  when  it  is  moving  at  the  rate  of  3  miles  an  hour..    If  the 
resistances  from  friction,  etc.,  are  8  pounds  per  ton,  how  many  foot- 
pounds of  work  have  been  expended  upon  the  car  ?     (First  find  the 
work  done  in  overcoming  friction,  etc.,  through  50  feet,  which  is  50 
foot-pounds x  10 x 8.     To  this,, add  the  work  done  in  giving  the  car 
kinetic  energy.) 

16.  Determine,  by  the  composition  of  forces,  whether  three  con- 
curring forces  with  magnitudes  of  5,  6,  and  12  pounds,  respectively, 
can  be  in  equilibrium. 

17.  Explain  why  a  soap-bubble  blown  at  one  end  of  a  tube  con- 
tracts, and  forces  a  current  of  air  out  of  the  other  end  of  the 
tube. 

18.  A  railway  train  moves  past  a  station  at  the  rate  of  20  miles  an 
hour.    A  mail  agent  throws  out  a  parcel,  in  a  direction  perpen- 
dicular to  the  track  and  with  a  horizontal  velocity  of  20  feet  per 
second.     Determine  the  velocity  of  the  parcel  at  the  beginning  of  its 
flight. 


92  SCHOOL   PHYSICS. 

19.  A  constant  force  acting  on  a  mass  of  15  grams  for  4  seconds 
gives  it  a  velocity  of  20  cm.  per  second.     Find  the  magnitude  of  the 
force  in  dynes. 

20.  A  250-pound  projectile   is  fired  from  a  12-ton  gun  with  an 
initial  velocity  of  1,420  feet  per  second.     Determine  the  velocity  of 
the  gun's  recoil. 

21.  What  is  the  centrifugal  force  of  a  20-pound  mass  moving  uni- 
formly once  in  5  seconds  around  a  circle  6  feet  in  diameter? 

22.  A  man  pushes  at  the  rear  of  a  street  car  and  in  the  line  of  its 
motion  with  a  force  of  50  pounds.      How  much  work  does  he  per- 
form while  the  car  moves  10  feet? 

23.  A  man  pushes  at  one  corner  of  the  rear  platform  of  a  street  car 
with  a  force  of  50  pounds,  and  in  a  direction  that  makes  an  angle  of 
45°  with  the  car's  line  of  motion.     How  much  work  does  he  perform 
while  the  car  moves  10  feet  ? 

24.  A  man  pushes  directly  against  the  side  of  a  street  car  with  a 
force  of  50  pounds.      How  much  work  does  he  perform  while   the 
car  moves  10  feet  along  the  track? 

25.  A  man  pushes  against  the  corner  of  the  front  platform  of  a 
street  car  with  a  force  of  50  pounds,  and  in  a  direction  that  makes 
an  angle  of  135°  with  the  track.     How  much  work  does  he  perform 
while  the  car  moves  forward  10  feet? 

26.  Determine   the   magnitude   of  the  kinetic   energy  of  a  body 
having  a  mass  of  50  pounds,  and  a  velocity  of  30  feet  per  second, 
(a)  in  gravitation  units ;  (6)  in  absolute  units. 

27.  If  a  man  does  1,056,000  foot-pounds  in  a  working  day  of  8 
hours,  what  horse-power  represents  his  working  power? 

Ans.  &  H.P. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Whirling  table  (Fig.  46)  and  attach- 
ments ;  wooden  blocks  ;  rubber  cord  ;  speed  counter. 

1.  Determine  the  ratio  between  the  circumferences  of  the  driver 
wheel  and  the  follower  (i.e.,  the  two  wheels  that  carry  the  belt)  of 
the  whirling  table  by  counting  the  revolutions  made  by  the  spindle,  c, 
while  the  large  wheel  revolves  once. 

2.  To  the  whirling  table,  attach  a  disk  on  which  rests  a  ball. 
Rotate  the  apparatus  and  make  a  record  of  the  consequent  phenome- 
non.    Connect  the  ball   by  a  stiff  elastic  cord  to  the  center  of  the 


WORK   AND   ENERGY. 


93 


disk.     Rotate  the  apparatus  with  increasing  speed,  and  make  a  note 
of  what  takes  place.     (See  Fig.  48.) 

3.  To  the  whirling  table,  attach  a  frame  carrying  two  tubes  contain- 
ing mercury  and  water,  and  supported  at  an 

angle,  as  shown  in  Fig.  49.  Rotate  the  ap- 
paratus rapidly,  and  make  a  record  of  any- 
thing peculiar  that  attracts  your  notice.  FlG  48 

4.  To  the  whirling  table,  attach  the  appa- 

ratus consisting  of  flexible  hoops,  as 
shown  in  Fig.  50.  The  hoops  are 
firmly  fixed  at  the  bottom,  but  the 
central  spindle  passes  freely  through 
FIG.  49.  the  holes  where  the  hoops  cross  each 

other  at  the  top.  Rotate  the  appa- 
ratus rapidly,  and  record  any  result  noticed  that  has  any  bearing 
on  the  shape  of  the  earth. 

5.  Replace  the  flexible  hoops  by  an  inflexible  iron  ring  about  a 
foot  in  diameter.     From  the  upper  point  of  this 

ring,  suspend  successively  a  skein  of  thread,  a 
looped  chain,  and  a  globular  glass  vessel  contain- 
ing some  mercury  and  some  ink-colored  water. 
In  each  case,  rotate  the  apparatus,  and  record 
your  observations,  as  you  are  supposed  to  do  in 
all  such  cases. 

6.  From  the  extremities  of  different  axes,  suc- 
cessively suspend  wooden  solids  of  various  geo- 
metrical forms ;  e.g.,  sphere,  oblate  spheroid,  prolate  spheroid,  cylin- 
der, etc.     Rotate  and  record  as,  before. 

7.  To  the  whirling  table,  attach  the  frame  carrying  two  balls  of 
equal  mass  (see  Fig.  46)  free  to  slide  on  a  wire,  and  connected  by  a 
thread.     By  trial,  find  a  position  for  the  balls  such  that  the  joined 
balls  will  be  on  opposite  sides  of  the  center  of  rotation,  and  yet  not 
slide  toward  either  end  of  the  wire  when  the  spindle  is  put  in  rapid 
rotation.     Measure  the  distance  of  each  ball  from  the  center  of  rota- 
tion.    What  is  the  tendency  of  each  ball  ?    What  case  under  com- 
position of  forces  is  thus  illustrated? 

8.  Change  the  balls  for  two  joined  balls  of  unequal  but  known 
masses.     Place  them  one  on  each  side  of  the  center  of  rotation,  and 
so  that  they  will  retain  their  positions  when  the  spindle  is  rapidly 
rotated.     When  these  positions  have  been  determined,  measure  the 


FIG.  50. 


94 


SCHOOL   PHYSICS. 


distances  from  the  center  of  rotation  to  the  centers  of  the  two  balls, 
arid  see  how  the  ratio  between  the  distances  compares  with  the  ratio 
between  the  masses  of  the  balls.  What  do  you  suppose  to  be  the 
purpose  ol  this  exercise? 

9.  Fig.  51  represents  a  very  valuable  attachment  for  the  whirling 
table.  A  ball  of  known  mass  slides  on  a  horizontal  wire.  To  this 
ball  is  attached  a  flexible  cord  that  turns  around  a  pulley  at  the  bot- 
tom, divides  into  two,  passes  over  the  pulleys  at  the  top,  and  carries 
adjustable  and  slotted  disk  weights.  The  middle  cord  passes  through 
the  slots  of  the  weights.  The  cord  and  the  center  of  the  disks  must 
lie  in  the  center  of  rotation.  Rotate  the  apparatus  with  gradually 
increasing  speed  until  the  outward  pull  of  the  ball  just  begins  to  lift 

the  load.  Keeping  this  speed  con- 
stant, count  the  number  of  revolu- 
tions that  the  driving  wheel  makes 
in  10  seconds.  Find  the  average  of 
several  such  trials.  Measure  the 
horizontal  distance  between  the  cen- 
ter of  the  ball  and  the  axis  of  rota- 
tion, and  thence  compute  the  velocity 
of  the  ball  in  the  recent  trials. 
Compare  the  result  with  the  formula 
given  in  §  78.  Repeat  the  experi- 
ment, using  a  "  speed  counter "  to 
determine  the  number  of  revolutions 
made  by  the  spindle  in  10  seconds,  and  computing  anew  the  velocity 
of  the  ball. 

Replace  the  ball  by  one  twice  as  heavy  and  at  the  same  distance 
from  the  center  of  rotation.  Double  the  load  carried  by  the  vertical 
cords.  Counting  as  before,  determine  the  rate  of  rotation  necessary 
to  lift  the  load.  Compare  the  result  with  the  first  law  given  in  §  78. 

Determine  the  load  that  may  be  lifted  by  the  ball  when  the  driver 
makes  twice  as  many  revolutions  as  before;  when  it  makes  three 
times  as  many  revolutions.  Compare  results  with  the  second  law 
given  in  §  78. 

Taking  any  of  these  trials  as  a  standard  for  comparison,  move  the 
ball  to  a  point  twice  as  far  from  the  center  of  rotation,  and  turn  the 
driving  wheel  half  as  fast.  How  will  the  two  velocities  of  the  ball 
compare?  At  this  slower  rate  of  rotation,  determine  the  load  that 
may  be  lifted.  Compare  the  result  with  the  third  law  given  in  §  78. 


FIG.  51. 


GRAVITATION. 


95 


Tabulate  all  of  your  results  as  usual. 

10.  Float  upon  water  two  blocks  of  wood,  one  of  which  is  twice  as 
heavy  as  the  other.      Connect  them  by  a  stretched  rubber    cord. 
Release  the  blocks,  and  they  will  move  toward  each  other,  but  with 
unequal  velocities.     Determine  how  much  faster  one  moves  than  the 
other,  and  compare  their  momenta. 

11.  On  a  page  of  cross-section  paper  (i.e.,  paper  ruled  in  squares 
1  mm.  or  0.1  inch  on  a  side,  which  can  be  purchased  at  nearly  any 
optician's)  select  arbitrarily  some  corner  of  a  square ;  mark  it  0,  and 
call  it  "the  origin  of  coordinates."      Mark   the  right-hand  end  of 
the  horizontal  line  passing  through  the  origin,  X,  and  the  left-hand 
end  of  the  same  line,  X'.     Call  the  line,  X'X,  "  the  axis  of  abscissas." 
Mark  the  upper  end  of  the  vertical  line  passing  through  the  origin,  Y, 
and  the  lower  end  of  the  line,  Y' .     Call  the  line,  Y'  Y,  "  the  axis  of 
ordinates."     From  0,  count  off,  on  the  axis  of  abscissas,  three  vspaces 
to  a  point,  which  mark  M.    On  the  vertical  line,  measure  two  spaces 
upward  to  a  point,  which  mark  P      The  distance  OM  is  called  "the 
abscissa  "  of  the  point,  P.     The  distance  MP  is  called  "  the  ordinate  " 
of  the  point,  P.    Negative  abscissas  would  be  measured  from  O  toward 
X',  and  negative  ordinates  would  be  drawn  downward  from  the  axis 
of  abscissas. 

Using  the    same   axes  of  coordinates,   locate  points  having   co- 
ordinates with  the  following  values:  — 


Points, 
a 
b 
c 
d 


Abscissas. 
-3 
-2 

0 

2 


Ordinates. 

12 

4 

0 

-1.3 


Points.  A  bscissas.  Ordinates. 

e  4  -2 

/  6  -2.4 

g  8  -2.67 

h  10  2.86 


Through  the  points  thus  located,  draw  a  line  with  as  nearly  uniform 
a  curve  as 


III.    GEAVITATION,  ETC. 

89.  Gravitation. — Every  particle  of  matter  in  the  uni- 
verse has  an  attraction  for  every  other  particle.  This 
attractive  force  is  called  gravitation. 


96 


SCHOOL   PHYSICS. 


(a)  Gravitation  is  unaffected  by  the  interposition  of  any  substance. 
During  an  eclipse  of  the  sun,  the  moon  is  between  the  sun  and  the 
earth.  But  at  such  a  time,  the  sun  and  earth  attract  each  other  with 
the  same  force  that  they  do  at  other  times. 

(6)  Gravitation  is  independent  of  the  kind  of  matter,  but  depends 
upon  the  quantity  or  mass,  and  the  distance.  Mass  does  not  mean 
size.  The  planet  Jupiter  is  about  1,300  times  as  large  as  the  earth, 
but  it  has  only  about  300  times  as  much  matter,  because  it  is  only 
0.23  times  as  dense. 

90.  Law  of  Gravitation.  —  The  mutual  attraction  between 
two  bodies  varies  directly  as  the  product  of  their  masses,  and 
inversely  as  the  square  of  the  distance  between  their  centers 
of  mass.  For  example,  doubling  this  product  doubles  the 
attraction  ;  doubling  the  distance,  quarters  the  attraction ; 
doubling  both  the  product  and  the  distance  halves  the 
attraction. 

(a)  Represent  the  attraction  between  two  units  of  mass  at  unit 
distance  by  a.  Then,  in  the  case  of  two  bodies  containing  respectively 
m  and  n  units  of  mass,  the  attraction  of  either  for  the  other  at  unit 
distance  will  be  mna.  If  the  distance  be  increased  to  d  units,  the 

attraction  will  be  ^ 

(&)  Notice  that  this  attraction  is  mutual. 
The  earth  draws  the  falling  apple  with  a 
force  that  gives  it  a  certain  momentum; 
the  apple  draws  the  earth  with  an  equal 
force,  that  gives  to  it  an  equal  momentum. 

91.  Gravity.  —  The  most  familiar 
illustration  of  gravitation  is  the 
attraction  between  the  earth  and 
bodies  upon  or  near  its  surface. 
This  particular  form  of  gravitation 
is  commonly  called  gravity.  Its 
measure  is  weight.  Its  direction  is 
that  of  the  plumb  line,  i.e.,  vertical. 


FIG.  52. 


UNIVERS; 

DEPARTMENT  OF 
GRAVITATION.  97 

92.  Weight. — As  the  mass  of  the  earth  remains  con- 
stant, doubling  the  mass  of  the  body  weighed  doubles  the 
product   of    the   masses,    and   consequently   doubles   the 
weight.     When  we  ascend  from  the  surface  of  the  earth, 
there  is  nothing  to  interfere  with  the  working  of  the  law 
of  universal  gravitation  ;  but  when  we  descend  below  the 
surface,  we  leave  behind  us  particles  of  matter  the  attrac- 
tion of  which  partly  counterbalances  that  of  the  rest  of  the 
earth.     The  weight  of  a  body  at  one  place  on  the  surface 
of   the  earth  differs   from   its  weight  at  another  place, 
because  the  earth  is  not  a  perfect  sphere  and  its  density 
is  not  uniform. 

93.  Law  of  Weight.  —  Bodies  weigh  most  at  the  surface 
of  the  earth.    For  bodies  in  the  earth's  crust,  the  weight  varies 
approximately  as  the  distance  from  the  center.     For  bodies 
above  the  earths  surface,  the  weight  varies  inversely  as  the 
square  of  the  distance  from  the  center. 

(a)  Let  the  heavy  black  line  of  Fig.  53  represent  a  spherical  shell 
of  uniform  thickness  and  density  with  bodies  at  c  and  e  within  the 
shell,  and  at  i  and  n,  without  the  shell. 
For  such   conditions,  these  propositions 
have  been  established  :  — 

(1)  The  attraction  of  the  matter  com- 
posing the  shell  draws  bodies  within  the 
shell,  as  at  c  and  e,  equally  in  all  direc- 
tions. 

(2)  The  attraction  of  the  matter  com- 
posing the  shell  pulls  bodies  outside  the 

shell,  as  at  t'-or  n,  just  as  it  would  if  the  FIG.  53. 

entire  mass  of  the  shell  were  concentrated 
at  its  center,  c. 

In  assuming  that  such  a  shell  with  a  radius  of  4,000  miles  repre- 
sents the  earth,  we  ignore  the  variation  between  polar  and  equatorial 
7 


98  SCHOOL   PHYSICS. 

diameters,  the  variation  in  the  density  of  the  earth's  crust,  and  the 
possible  variation  of  its  thickness.  Still,  make  the  assumption. 
Then,  at  a  depth  of  15  miles,  a  body  weighing  100  pounds  at  the 
surface  would  weigh  about  100  pounds  x  f  j$$.  At  an  elevation  of 
4,000  miles  above  the  surface  (8,000  miles  from  the  center),  it  would 

40002 

weigh  100  pounds  x  -  — —  =  25  pounds. 

oUOU 

CLASSROOM   EXERCISES. 

1.  Suppose  the  earth  to  be  solid.      How  far  below  the  surface 
would  a  10-pound  ball  weigh  only  4  pounds  ? 

Solution.  —  As  the  weight  is  to  be  reduced  six  tenths,  it  must  be 
carried  0.6  of  the  way  to  the  center. 

Ans.  4,000  miles  x  0.6  =  2,400  miles. 

2.  On  the  same  supposition,  what  would  a  body  weighing  550 
pounds  on  the  surface  of  the  earth  weigh  3,000  miles  below  the  sur- 
face? A  ns.  137^  pounds. 

3.  Two  bodies  attract  each  other  with  a  certain  force  when  they 
are  75  m.  apart.     How  many  times  will  the  attraction  be  increased 
when  they  are  50  m.  apart?  Ans.  2£. 

4.  Given  three  balls.     The  first  weighs  6  pounds,  and  is  25  feet 
distant  from  the  third.     The  second  weighs  9  pounds,  and  is  50  feet 
distant  from  the  third,     (a)  Which  exerts  the  greater  force    upon 
the  third?     (&)  How  many  times  as  great?  Ans.  f. 

5.  A  body  at  the  earth's  surface  weighs  900  pounds.     What  would 
it  weigh  8,000  miles  above  the  surface  ? 

6.  How  far  above  the  surface  of  the  earth  will  a  pound  avoirdu- 
pois weigh  only  an  ounce  ?  Ans.  12,000  miles. 

7.  At  a  height  of  3,000  miles  above  the  surface  of  the  earth,  what 
would  be  the  difference  in  the  weights  of  a  man  weighing  200  pounds 
and  of  a  boy  weighing  100  pounds?  Ans.  32.65  pounds. 

8.  Find  the  weight  of  a  180-pound  ball  2,000   miles   above  the 
earth's  surface. 

9.  (a)  If  the  earth  was  solid,  would  a  50-pound  cannon  ball  weigh 
more  1,000  miles  above  the  earth's  surface,  or  1,000  miles  below  it? 
(&)  How  much  ? 

10.  If  the  moon  was   moved  to  three  times  its  present  distance 
from  the  earth,  what  would  be  the  effect  (a)  on  its  attraction  for  the 
earth  ?     (6)  On  the  earth's  attraction  for  it  ? 

11.  A  team  pulling  northeast  with  a  force  of  800  pounds,  moves  a 


GRAVITATION.  99 

railway  car  12  feet  along  a  track  running  north.     How  much  work  is 
done  by  the  team  ? 

12.  How  far  above  the  surface  ot  the  earth  must  2,700  pounds  be 
placed  to  weigh  1,200  pounds?  Ans.  2,000  miles. 

13.  What  effect  would  it  have  on  the  weight  of  a  body  to  double 
the  mass  of  the  body  and  also  to  double  the  mass  of  the  earth?       , 

14.  A  50-pound  ball  moving  with  a  velocity  of  75  feet  per  second 
strikes  a  200-pound  ball  squarely,  and  rebounds  with  a  velocity  of  25 
feet.    What  velocity  was  given  to  the  200-*pound  ball  by  the  collision  ? 

94.  Center  of  Mass.  —  A  body's  center  of  mass  is  the 
point  about  which  all  the  matter  composing  the  body  may 
be  balanced.  It  is  also  called  the  center  of  inertia.  In 
some  cases  it  is  also  the  center  of  gravity. 

(a)  The  force  of  gravity  tends  to  draw  every  particle  of  matter 
toward  the  center  of  the  earth,  or  downward  in  a  vertical,  line.  We 
may,  therefore,  consider  the  effect  of  this  force  upon  any  body  as  the 
sum  of  an  almost  infinite  number  of  parallel  forces,  each,  of  which  is 
acting  upon  one  of  the  particles  of  which  that  body  is  composed. 
We  may  also  consider  this  sum  of 
forces,  or  total  gravity,  as  a  result- 
ant force,  GP,  acting  upon  a  single 
point,  just  as  the  force  exerted  by  two 
horses  harnessed  to  a  whiffletree  is 
equivalent  to  another  force  equal  to 
the  sum  of  the  forces  exerted,  by  the 
horses,  and  applied  at  a  single  point  at 
or  near  the  middle  of  the  whiffletree. 
This  single  point,  G,  which  may  be  re- 
garded as  the  point  of  application  of 
the  force  of  gravity  acting  upon  a  body, 
is  called  the  center  of  mass  of  that  FlG  54 

body  ;  in  other  words,  the  weight  of  a 
body  and  its  mass  may  be  considered  as  concentrated  at  a  single  point. 

(&)  When  a  body  is  acted  on  by  any  force,  there  is,  owing  to  the 
inertia  of  each  particle,  a  series  of  reactions  in  the  opposite  direction, 
the  resultant  of  which  has  its  application  at  a  point  called  the  center 
of  inertia. 


100 


SCHOOL  PHYSICS. 


(c)  Any  force  acting  on  a  body  at  its  center  of  mass  tends  to  pro- 
duce a  motion  of  translation  in  the  direction  of  that  force ;  but,  if  the 
force  acts  on  the  body  at  any  other  point,  it  and  the  reaction  at  the 
center  of  mass  form  a  couple  that  tends  to  produce  rotary  motion  ot 
the  body. 

(d)  In  a  freely  falling  body,  no  matter  how  irregular  its  form  or 
how  indescribable  the  curves  made  by  any  ot  its  projecting  parts, 
the  line  of  direction  in  which  the  center  of  mass  moves  is  a  vertical 
line. 

95.  To  find  the  Center  of  Mass.  — In  a  body  suspended 
from  a  point,  the  center  of  mass  will  be  brought  as  low  as 
possible,  and  will,  therefore,  lie  in  a  vertical  line  drawn 
through  the  point  of  support.  This  fact  affords  a  ready 
means  of  determining  this  point  experimentally. 

(a)  Let  any  irregularly  shaped  body,  as  a  stone  or  chair,  be  sus- 
pended so  as  to  move  freely.  Drop  a  plumb  line  from  the  point  of 

suspension,  and  make  it  fast  or  mark 
its  direction.  The  center  of  mass 
will  lie  in  this  line.  From  a  second 
point,  not  in  the  line  already  deter- 
mined, suspend  the  body;  let  fall  a 
plumb  line  as  before.  The  center  of 
mass  will  lie  in  this  line  also.  But  to 
lie  in  both  lines,  it  must  lie  at  their 
intersection. 

(&)  If  a  flat  piece  of  cardboard  can 
be  balanced  on  the  point  of  a  pin,  its 
center  of  mass  lies  vertically  above  the 
point  of  support,  midway  between  the 
two  sides  of  the  cardboard.  When  a 
body  is  of  uniform  density  and  regular 
shape,  its  center  of  mass  and  its  center 
of  figure  will  coincide  $  e.g.,  the  center 
of  mass  of  a  sphere  of  uniform  density  is  at  its  center  of  volume. 


FIG.  55. 


96.    May  be  Outside  the   Body.  —  In  some  bodies,  as  a 
ring  or  box  or  hollow  sphere  or  cask,  the  center  of  mass 


GRAVITATION.  ', 

does  not  lie  in  the  matter  of  which  the  body  is  com- 
posed. 

(a)  This  fact  may  be  illustrated  by  the  "  balancer,"  represented  in 
Fig.  56.  The  center  of  mass  lies  a  little  above  the  line  joining  the 
two  heavy  balls,  and  thus  under  the  foot  of 
the  waltzing  figure.  But  the  point,  wherever 
found,  will  have  the  same  properties  as  if  it 
lay  in  the  mass  of  the  body. 

97.  The  Base.  —  The  side  on  which 
a  body  rests  is  called  its  base.     If  the 
body  is  supported  on  legs,  as  a  chair, 
the   base   is   the    polygon   formed  by 
joining  the  points  of  support. 

98.  Equilibrium.  —  A    body    sup- 
ported at  a  single  point  will  rest  in 
equilibrium  when  a  vertical  line  pass 

,,  ,  n,  .  FIG.  56. 

ing  through  its  center  01  mass,  i.e., 
the  line  of  direction,  also  passes  through  the  point  of 
support.  A  body  supported  on  a  surface  will  rest  in 
equilibrium  when  the  line  of  direction  (§  94,  d)  falls 
within  its  base.  In  general  terms,  a  body  is  in  equilib- 
rium when  the  resultant  of  all  the  forces  acting  on  it  is 
zero.  The  center  of  mass  will  be  supported  when  it  coin- 
cides with  the  point  of  support,  or  is  in  the  same  vertical 
line  with  it.  When  the  center  of  mass  is  supported, 
the  whole  body  is  supported  and  rests  in  a  state  of 
equilibrium. 

(a)  When  the  line  of  direction  falls  without  the  base,  weight  and 
reaction  of  support  become  forces  that  form  a  couple  and  overturn 
the  body. 


SCHOOL   PHYSICS. 

Experiment  52.  —  With  the  point  of  a  penknife  blade,  make  a  hole 
of  2  or  3  mm.  diameter  in  the  large  end  of  an  egg.  In  the  small  end, 
prick  a  pinhole.  Blow  the-  contents  of  the  shell  out  through  the 
larger  hole.  Rinse  and  dry  the  shell.  Drop  a  little  pulverized  rosin 
or  melted  sealing  wax  through  the  larger  hole  into  the  smaller  end  of 
the  egg.  Support  the  egg  in  a  small  tin  can  (that  may  be  obtained 
from  any  kitchen)  or  in  any  other  convenient  way,  and  pour  a  few 
grams  of  melted  lead  through  the  larger  hole  and  into  the  smaller  end. 
The  lead  will  not  run  out  through  the  pinhole  even  if  the  rosin  or 
sealing  wax  is  not  used.  The  larger  hole  may  be  neatly  concealed 
with  a  piece  of  thin  paper  put  on  with  flour  paste.  Try  to  make  your 
"  magical  egg  "  lie  on  its  side. 

99.  Kinds  of  Equilibrium.  —  There  are  three  kinds  of 
equilibrium :  — 

(1)  A  body  supported  in  such  a  way  that,  when  slightly 
displaced  from  its  position  of  equilibrium,  it  tends  to  return 
to  that  position,  is  said  to  be  in  stable  equilibrium.     Such  a 
displacement  raises  the  center  of  mass. 

(2)  A  body  supported  in  such  a  way  that,  when  slightly 
displaced  from  its  position  of  equilibrium,  it  tends  to  fall 
further  away  from  that  position,  is  said  to  be  in  unstable 
equilibrium.     Such  a  displacement  lowers  the  center  of 
mass. 

(3)  A  body  supported  in  such  a  way  that,  when  displaced 
from  its  position  of  equilibrium,  it  tends  neither  to  return  to 
its  former  position  nor  to  fall  further  from  it,  is  said  to  be 
in  neutral  or  indifferent  equilibrium.     Such  a  displacement 
neither  raises  nor  lowers  the  center  of  mass. 

100.  Stability.  —  When  the  line  of  direction  falls  within 
the  base,  the  body  stands ;  when  without  the  base,  the  body 
falls  over.     The  stability  of  a  body  is  measured  by  the 
amount  of  work  that  must  be  done  to  overturn  it.     This 


GRAVITATION.  103 

amount  may  be  increased  by  enlarging  the  base,  01  by 
lowering  the  center  of  mass,  or  both. 

(a)  Let  Fig.  57  represent  the  vertical  section  of  a  brick  placed 
upon  its  side,  its  position  of  greatest  stability.  In  order  to  stand 
the  brick  upon  its  end,  g,  the  center 
of  mass,  must  pass  over  the  edge,  c  ; 
that  is  to  say,  the  center  of  mass 


must  be  raised  a  distance  equal  to  a 

the  difference  between  ga  and  gc,  FlG-  57- 

or  the  distance,  nc.  But  to  lift  g  this  distance  is  the  same  as  to  lift 
the  whole  brick  vertically  a  distance  equal  to  nc.  Draw  similar 
figures  for  the  brick  when  placed  upon  its  edge  and  upon  its  end.  In 
each  case,  make  gn  equal  to  ga,  and  see  that  the  value  of  nc  decreases. 
But  nc  represents  the  distance  that  the  brick,  or  its  center  of  mass, 
must  be  raised,  before  the  line  of  direction  can  fall  without  the  base 
and  the  body  be  overturned.  To  lift  the  brick,  or  its  center  of  mass, 
a  small  distance  involves  less  work  than  to  lift  it  a  greater  distance. 
Therefore,  the  greater  the  value  of  nc,  the  more  work  required  to 
overturn  the  body,  or  the  greater  its  stability.  But  this  greater  value 
of  nc  evidently  depends  upon  a  larger  base,  a  lower  position  for  the 
center  of  mass,  or  both. 

(6)  When  the  body  rests  upon  a  point,  as  does  the  sphere,  or  upon 
a  line,  as  does  the  cylinder,  a  very  slight  force  is  sufficient  to  move  it, 
no  elevation  of  the  center  of  mass  being  necessary. 

CLASSROOM  EXERCISES. 

1.  Why  does  a  person  stand  less  firmly  when  his  feet  are  parallel 
and  close  together  than  when  they  are  more  gracefully  placed  ? 

2.  Why  can  a  child  walk  more  easily  with  a  cane  than  without  ? 

3.  Why  will  a  book  placed  on  a  desk-lid  stay  there,  while  a  marble 
will  roll  off? 

4.  Why  is  a  ton  of  stone  on  a  wagon  less  likely  to  upset  than  a  ton 
of  hay  similarly  placed  ? 

5.  If  a  falling  body  near  the  surface  of  the  earth  gains  an  accelera- 
tion of  32.16  feet,  what  would  be  its  acceleration  240,000  miles  from 
the  center  of  the  earth  ? 

6.  A  body  is  simultaneously  acted  upon  by  two  forces,  one  of  which 
would  give  it  a  velocity  of  100  feet  per  second  northward,  while  the 


104  SCHOOL   PHYSICS. 

other  would  give  it  a  northeasterly  velocity  of   75  feet  per  second. 
Determine  the  magnitude  and  direction  of  the  resultant  velocity. 

7.  A  given  force,  acting  for  ten  minutes  upon  a  body  weighing  100 
pounds,  produces  a  velocity  of  a  mile  a  minute.     Determine  the  mag- 
nitude of  the  force  in  poundals. 

8.  How  many  gallons  of  water,  each  weighing  8  pounds,  can  a  100- 

horse-power  engine  raise  to  a  height  of  200  feet 
in  10  hours  ? 

9.  Why  have  the  Egyptian  pyramids   great 
stability  ? 

10.  Why  is  it  easier  for  a  baby  elephant  than 
for  a  baby  boy  to  learn  to  walk  ? 

11.  Where  is  the  axis  of  rotation  of  a  carriage 
wheel?     Where  should  the  center  of  mass  of  a 
carriage  wheel  be  ? 

12.  A  boy  placed  a  step-ladder  as  shown  in 
Fig.  58,  and  it  stood.     Why?    He  then  climbed 

to  its  top,  and  it  fell.     Why? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Plumb  bob;   chalk;   cardboard;   box 
as  described  below ;  screw-eye  ;  mortar. 

1.  Drive  small  tacks  into  the  frame  of  a  slate  at  adjacent  corners. 
Tie  the  middle  of  a  stout  thread  to  one  of  the  tacks.     Fasten  a  small 
weight  to  one  end  of  the  thread,  and  support  the  apparatus  from  the 
other  end.     Mark  on  the  slate  the   direction   in  which  the  thread 
crosses  it.     Similarly  support  the  slate  by  the  other  tack,  and  mark 
the  direction  of  the  thread  by  another  line.     Place  the  intersection  of 
the  two  lines  over  the  end  of  the  finger,  and  see  if  the  slate  is  bal- 
anced.    The  point  thus  located  approximately  represents  what? 

2.  Cut  a  rectangle   from   cardboard.      Draw   its   two   diagonals. 
Balance  the  cardboard  to  see  how  near  the  center  of  mass  coincides 
with  the  center  of  area.     Can  the  center  of  mass  lie  on  the  surface 
of  such  a  body  ? 

3.  Drive  a  wire  nail  into  a  vertical  support,  and  cut  off  the  head  of 
the  nail.     Bore  several  holes  through  an  irregularly  shaped  board 
near  its  edges.     Using  one  of  these  holes,  hang  the  board  on  the  nail. 
From  the  nail^hang  a  chalked  plumb  line.     When  the  plumb  line  has 
come  to  rest,  "  snap "  it  so  as  to  make  a  vertical  line  on  the  board. 
Change  the  position  of  the  board,  the  nail  passing  through  another 


GRAVITATION.  105 

of  the  holes.  Chalk  the  line,  suspend  and  "snap"  as  before.  Place 
the  intersection  of  the  two  chalk  lines  over  the  end  of  the  finger,  and 
see  if  the  board  then  balances.  Using  another  hole,  similarly  chalk 
another  line,  and  see  if  the  three  lines  have  a  common  point  of  inter- 
section. 

4.  Fill  a  box,  about  2x4x8  inches  (a  shallow  cigar  box  will  do), 
with  stiff  mortar,  and  nail  down  the  cover.  Stand  it  on  end,  so  that 
the  8"  edges  will  be  vertical.  (It  is  common  for  architects  and 
mechanics  to  indicate  "feet"  by  one  tick,  and  "inches  "  by  two  ticks, 
as  in  the  preceding  sentence.)  Insert  a  small  screw-eye  or  hook  at  the 
middle  of  one  of  the  4"  x  8"  surfaces ;  it  will  be  approximately  on  a 
level  with  the  center  of  mass.  Tack  a  small  wooden  strip  to  the 
table,  at  the  foot  of  this  side,  to  keep  the  box  from  slipping  when 
pulled.  Tie  one  end  of  a  cord  to  this  screw-eye,  and  the  other  end  to 
the  hook  of  a  spring-balance.  Hold  the  dynamometer  so  that  its  axis 
and  the  string  lie  in  a  straight  line  that  is  perpendicular  to  the  side 
of  the  box.  Carefully  observing  the  scale  of  the  dynamometer,  pull 
steadily  until  the  box  falls  over.  Record  the  maximum  reading  of 
the  scale.  On  one  of  the  2"  x  8"  faces,  draw  and  bisect  a  diagonal. 
What  is  the  difference  between  half  the  length  of  the  diagonal  and 
half  the  height  of  the  box  as  it  was  standing?  Record  that  differ- 
ence. What  does  it  represent? 

Instead  of  using  the  spring-balance,  one  may  pass  the  cord  over  a 
pulley  adjusted  at  the  level  of  the  screw-eye,  attach  a  scale-pan  of 
known  weight  to  the  free  end  of  the  cord,  and  add  weights  until  the 
box  begins  to  overturn. 

If  the  screw-eye  pulls  out,  pass  a  cord  or  wire  around  the  box  at 
the  proper  level,  and  attach  the  other  cord  to  it  at  the  proper  place. 
A  wire  with  a  loop  at  one  end  may  be  passed  through  the  box  from 
one  face  to  the  opposite  side,  and  there  made  fast  before  filling  the 
box.  The  loop  will  then  take  the  place  of  the  screw-eye.  It  is 
especially  desirable  thus  to  connect  the  opposing  2"  x  4"  and  the 
2"  x  8"  faces. 

Place  the  box  so  that  its  4"  edges  shall  be  vertical.  Ascertain  and 
record  the  force  necessary  to  overturn  the  box  by  a  horizontal  pull,  as 
before.  On  one  of  the  2"  x  4"  faces,  draw  and  bisect  a  diagonal. 
Find  how  much  the  semi-diagonal  exceeds  2",  the  semi-altitude  of  the 
box.  Record  this  difference. 

Transfer  the  screw-eye  to  the  middle  of  one  of  the  2"  x  8"  sides, 
and  place  the  box  with  its  8"  edges  vertical.  Ascertain  and  record 


106  SCHOOL  PHYSICS. 

the  force  necessary  to  overturn  the  box,  as  before.  On  one  of  the 
4"  x  8"  faces,  draw  and  bisect  a  diagonal.  Find  how  much  the  semi- 
diagonal  exceeds  4",  the  semi-altitude.  Record  this  difference. 

Place  the  box  so  that  its  2"  edges  shall  be  vertical.  Ascertain  and 
record  the  force  necessary  to  overturn  the  box,  as  before.  Find  how 
much  the  semi-diagonal  of  the  2"  x  4"  face  exceeds  1",  the  semi- 
altitude.  Record  this  difference. 

Transfer  the  screw-eye  to  the  middle  of  one  of  the  2"  x  4"  sides, 
and  place  the  box  with  its  4"  edges  vertical.  Ascertain  and  record 
the  force  necessary  to  overturn  the  box,  as  before.  Find  how  much 
the  semi-diagonal  of  a  4"  x  8"  face  exceeds  2",  the  semi-altitude,  and 
record  that  difference. 

Place  the  box  so  that  its  2"  edges  shall  be  vertical.  Ascertain  and 
record  the  force  necessary  to  overturn  the  box,  as  before.  Find  how 
much  the  semi-diagonal  of  the  2"  x  8"  surface  exceeds  1",  the  semi- 
altitude,  and  record  that  difference. 

Weigh  the  box.  Multiply  its  weight  by  the  excess  of  the  semi- 
diagonal  over  the  semi-altitude  in  each  case.  What  do  these  products 
represent?  What  do  they  measure?  If  weight  is  measured  in 
pounds  and  decimals  thereof,  and  diagonals  and  altitudes  in  feet  and 
decimals  thereof,  these  products  will  represent  what  kind  of  units  ? 
Compare  these  several  products  with  the  corresponding  forces  used 
in  overturning  the  box.  Do  you  discover  any  relation  between  them  ? 

5.  Cut  a  piece  of  board  20"  long,  3"  wide  at  one  end,  and  7" 
wide  at  the  other  end.  Find  a  point  on  the  surface  of  the  board 
as  near  as  possible  to  the  center  of  mass,  and  over  it  paste  a  patch  of 
black  paper  an  inch  in  diameter.  On  the  same  side  of  the  board, 
and  a  foot  or  so  from  the  other  paper,  paste  a  patch  of  red  paper 
about  2"  in  diameter.  Toss  the  board  up  edgewise  in  the  open  air, 
so  that  it  will  turn  end  over  end,  carefully  observing  the  motion  of 
the  two  paper  patches  relative  to  each  other.  Record  and  explain 
what  you  see. 


IV.    FALLING   BODIES. 

101.  Freely  Falling  Bodies.  —  When  a  body  is  left  un- 
supported and  free  to  move  under  the  influence  of  the 
force  of  gravity  and  without  any  resistance,  it  is  a  freely 
falling  body. 


FALLING  BODIES. 


107 


(a)  Unless  the  body  falls  from  a  very  great  ^height,  the  change  in 
the  intensity  of  the  attraction  due  to  the  change  of  distance  from  the 
center  of  the  earth  is  so  small  that  it  may,  without  sensible  error,  be 
disregarded.  It  is,  therefore,  common  to  consider  gravity  a  constant 
force ;  hence,  if  we  ignore  the  resistance  of  the  air,  the  laws  for  fall- 
ing bodies  will  be  the  same  as  for  uniformly  accelerated  motion. 

Experiment  53.  —  From  the  upper  window,  drop  simultaneously 
an  iron  and  a  wooden  ball  of  the  same  size.  Be  careful  that  your 
fingers  do  not  "  stick  "  to  one  ball  longer  than  to  the  other.  Notice 
that  the  two  balls  of  different  weight  strike  the  ground  at  practically 
the  same  time. 

102.  Velocities  of  Falling  Bodies.  —  When  a  feather  and 
a  cent  are  dropped  from  the  same 
height,  the  cent  reaches  the  ground 
first.  This  is  not  because  the  cent 
is  heavier,  but  because  the  feather 
meets  with  more  resistance  from 
the  air  in  proportion  to  its  mass. 
If  this  resistance  can  be  removed 
or  equalized,  the  two  bodies  will 
fall  equal  distances  in  equal  times, 
or  with  the  same  velocity.  The 
resistance  may  be  avoided  by  drop- 
ping them  in  a  glass  tube  from  which 
the  air  has  been  removed.  The  re- 
sistances may  be  nearly  equalized  by 
making  the  two  falling  bodies  of 
the  same  size  and  shape  but  of  dif- 
ferent weights,  as  in  the  preceding 
experiment. 

FIG.  59. 
Experiment  54.  —  Tack  a  strip  of  wood 

half  an  inch  square  to  the  straight  edge  of  a  plank  16  feet  long. 


108  SCHOOL  PHYSICS. 

Fasten  metal  strips  an  inch  wide  to  the  sides  of  the  wooden  strip 
so  as  to  make  a  double-track  way  which  should  be  straight  and 
smooth.  Divide  the  edge  of  the  plank  on  one  side  of  the  track  into 
16  foot-spaces,  plainly  marked.  Raise  one  end  of  the  plank  a  foot 
higher  than  the  other.  Place  a  glass  or  an  iron  ball  at  the  top  of 
the  inclined  track.  Notice  how  often  the  classroom  clock  ticks  in  a 
second.  Place  a  finger  on  top  of  the  ball,  thus  holding  it  ready  for  a 
start.  Repeat  the  word  "  tick  "  in  unison  with  the  clock  until  you 
"  feel  "  the  rhythm  of  its  swing,  and,  just  at  the  moment  of  a  "  tick," 
lift  the  finger  from  the  ball,  which  will  begin  to  roll  down  the  track. 
Notice  and  record  the  position  of  the  ball  at  the  end  of  successive 
seconds.  To  locate  the  ball  at  the  end  of  the  allotted  period,  place 
on  the  upper  side  of  the  half-inch  strip  a  wooden  block  just  wide 
enough  to  hold  its  position,  and  just  thick  enough  to  produce  an 
easily  audible  click  when  struck  by  the  ball.  By  trial,  place  this 
block  so  that  the  tick  and  the  click  shall  coincide.  Repeat  your  ob- 
servations, and  average  the  results  of  similar  trials.  The  greater 
the  number  of  carefully  conducted  trials,  the  more  valuable  will  be 
your  averages. 

The  ball  will  roll  down  the  inclined  plane,  about  1  foot  in  the 
first  second,  4  feet  in  2  seconds,  9  feet  in  3  seconds,  16  feet  in  4 
seconds,  etc.  The  average  results  may  be  tabulated  as  follows  :  — 

Number  of         Spaces  fallen          Velocities  at  the  End          Total  Number  of 
Seconds.  each  Second.  of  each  Second.  Spaces  fallen. 

112  1 

234  4 

35                                  6  9 

47                                 8  16 

/                    2<-l                              2t  t* 

Representing  the  velocity  gained  each  second  (acceleration)  by  a, 
and,  consequently,  the  value  of  each  of  our  spaces  by  £  a,  we  have, 
from  the  above,  the  already  familiar  formulas,  V  =  \a  (2z  —  1);  v  =  at; 
(see  §  54). 


103.  Unimpeded  Fall.  —  By  giving  a  greater  inclination 
to  the  plane  used  in  Experiment  54,  the  ball  will  roll 
more  rapidly,  and  our  unit  of  space  will  increase  from  one 
foot,  as  supposed  thus  far,  to  two,  three,  four,  or  five  feet, 


FALLING  BODIES.  109 

and  so  on ;  but  the  number  of  such  spaces  will  remain  as 
indicated  in  the  table  above.  By  disregarding  the  resist- 
ance of  the  air,  we  may  say  that  when  the  plane  becomes 
vertical,  the  body  becomes  a  freely  falling  body.  Our 
unit  of  space  has  now  become  16.08  feet,  or  490  centi- 
meters. It  will  fall  this  distance  during  the  first  second, 
three  times  this  distance  during  the  next  second,  five 
times  this  distance  during  the  third  second,  and  so  on. 

104.  Galileo's  Device. —  The  laws  of  accelerated  motion, 
as   given   in    §  55,  were  first  experimentally  verified  by 
Galileo.     To  avoid  the  difficulty  of  accurate  observation  of 
the  very  rapid  motion  of  a  freely  falling  body,  he  used  an 
inclined  plane,  down  the  groqved  edge  of  which  a  heavy 
ball  was  made  to  roll. 

(a)  Let  AB  represent  a  plane  so  inclined  that  the  velocity  of  a 
body  rolling  from  B  toward  A  will  be  readily  observable.  Let  C  be 
a  heavy  ball.  The  gravity  of  the  ball  may  be  represented  by  the  ver- 
tical line,  CD.  But  CD  may  be  resolved  into  CF,  which  represents  a 
force  acting  perpendicular  to  the  plane  and  producing  pressure  upon 
it  but  no  motion  at  all,  and  CE, 
which  represents  a  force  acting  par- 
allel to  the  plane,  the  only  force  of 
any  effect  in  producing  motion. ,  It 
may  be  shown  geometrically  that 

EC:CD::BG:BA. 
By  reducing,  therefore,  the  inclina- 
tion of  the  plane,  we  may  reduce  the 
magnitude  of  the  motion-producing 

component  of  the  force  of  gravity,  and  thus  reduce  the  velocity.  This 
will  not  affect  the  laws  of  the  motion,  that  motion  being  changed 
only  in  amount,  not  at  all  in  character. 

105.  Atwood's  Device. —  The  At  wood  machine  consists 
essentially  of  a  wheel  or  pulley,  R,  over  the  grooved  edge 


110  SCHOOL  PHYSICS. 

of  which  are  balanced  two  equal  weights  suspended  by  a 
long  silk  thread  which  is  both  light  and  strong.  The  axle 

of  this  wheel  is  preferably  sup- 
ported upon  the  circumferences 
of  four  friction  wheels,  r,  r,  r',  r', 
for  greater  delicacy  of  motion. 
As  the  thread  is  so  light  that 
its  weight  may  be  disregarded, 
it  is  evident  that  the  weights 
will  be  in  equilibrium  whatever 

FIG.  HI.  ,T     .  ...  mi  . 

their  position.     This   apparatus 

is  supported  upon  a  pillar  seven  or  eight  feet  high.  A 
weight  or  rider  placed  upon  one  of  the  weights  pro- 
duces motion  with  a  moderate  but  uniformly  accelerated 
velocity. 

(a)  Suppose  that  the  balanced  masses  weigh  49.5  grams  each,  and 
that  the  rider  weighs  1  gram.  The  total  mass  moved  is  100  grams,  and 
the  force  acting  is  the  weight  of  1  gram.  When  this  force  of  1  gram 
moves  a  mass  of  1  gram  (freely  falling  body),  it  produces  a  velocity 
too  great  for  easy  observation ;  when  the  same  force  acts  on  the  mass 
100  times  as  great,  it  produces  a  velocity  only  T£7  as  great  as  it  pro- 
duced in  the  other  case,  when  the  gram  mass  fell  alone.  Thus  we  may 
produce  variations  in  acceleration  as  we  desire. 

106.  Acceleration  Due  to  Gravity.  —  In  the  latitude  of 
New   York,   a   freely   falling   body   gains   a   velocity   of 
32.16  feet,   or    980   centimeters,  during  the  first  second 
of  its  fall.     It  makes  a  like  gain  of  velocity  during  each 
subsequent  second  of  its  fall.      This  distance  is,  therefore, 
called  the  acceleration  due  to  gravity,  and  is  generally  repre- 
sented ly  the  letter  g. 

107.  Formulas  for  Falling  Bodies.  —  Since  the  motion  of 
a  freely  falling  body  is  uniformly  accelerated  motion,  the 


FALLING  BODIES.  Ill 

formulas  for  freely  falling  bodies  may  be  derived  from 
those  for  uniformly  accelerated  motion  (§  54)  by  substitut- 
ing the  definite  quantity,  </,  for  the  indefinite  quantity,  a. 
Hence,  we  have  for  bodies  starting  from  rest  :  — 

(1)  V=fft. 

(2)  J'  =  j£(2*-l). 

(3)  l  = 


(a)  For  bodies  rolling  down  an  inclined  plane,  these  formulas 
may  be  made  applicable  by  multiplying  the  value  of  g  by  the  ratio 
between  the  height  and  the  length  of  the  plane. 

(&)  If  t  =  1,  formula  (1)  becomes  v  —  g;  i.  e.,  the  velocity  of  a  body 
falling  freely  for  one  second  from  a  state  of  rest  equals  the  acceleration. 

(c)  If  t  =  1,  formula  (3)  becomes  I  —  \g,  i.e.,  the  space  traversed 
in  a  second  by  a  body  freely  falling  from  a  state  of  rest  equals  half  of 
the  acceleration. 

(d)  From  formula  (1)  we  derive  the  value,  t  =  -.     Substituting 

g 

this  value  in  formula  (3),  we  have  I  =  \g  x  —  =  —  .     Hence,  v  =  V2  gl, 

9      '29 

showing  that  the  velocity  of  a  falling  body  varies  as  the  square  root 
of  the  distance  it  has  fallen. 

{e}  Xone  of  these  formulas  involve  any  expression  for  mass,  thus 
indicating  that  the  velocity  of  a  falling  body  is  not  affected  by  its 
mass. 

108.  Laws  of  Falling  Bodies.  —  For  bodies  starting 
from  rest,  these  formulas  may  be  translated  as  follows  :  — 

(1)  The  velocity  of  a  freely  falling  body  at  the  end  of 
any  second  of  its  descent  is  equal  to  32.16  feet  (980  cm.) 
multiplied  by  the  number  of  the  second. 

(2)  The  distance  traversed  by  a  freely  falling  body  dur- 
ing any  second  of  its  descent  is  equal  to  16.08  feet  (490  cm.) 
multiplied  by  one  less  than  twice  the  number  of  the  second. 

(3)  The  distance  traversed  by  a  freely  falling  body  dur- 


112  SCHOOL  PHYSICS. 

m 

ing  any  number  of  seconds  is  equal  to  16.08  feet  (490  cm.) 
multiplied  by  the  square  of  the  number  of  seconds. 

109.  Initial  Velocity  of  Falling  Bodies.  —A  body  may 
be  thrown  downward  as  well  as  dropped.  In  such  a  case 
the  effect  of  the  throw  must  be  added  to  the  effect  of 
gravity. 


110.  Bodies  thrown  Upward.  —  When  a  body  is  thrown 
vertically  upward,  gravity  diminishes  its  velocity  every 
second  by  g.     The  time  of  the  ascent  may  be  found  by 
dividing  the  initial  velocity  by  the  acceleration  of  gravity  : 

t=V~. 

9 

Projectiles. 

Experiment  55.  —  From  a  strip  of  wood  shaped  like  a  meter  stick 
or  common  lath,  cut  a  piece  about  10  cm.  long.  Cut  equal  notches  at 
two  corners,  a  and  e,  as  shown  in  Fig.  62.  Nail  the  middle  of  this 
piece  across  the  end  of  the  rest  of  the  lath,  thus  making  a  T-shaped 
form.  Clamp  the  other  end  of  the  long  leg  firmly  in  a  vise  so  that 
the  edge,  ae,  and  the  corresponding  edge  of  the  long  piece,  shall  be 
horizontal  and  several  feet  above  a  level  floor.  Place  lead  bullets  at 
a  and  e.  Strike  the  long  piece  a  sharp,  hori- 
zontal blow  near  the  cross-piece.  One  of  the 
bullets  will  be  shot  horizontally,  and  the 
;  —  other  will  be  dropped  nearly  vertically. 

Will  the  bullets  strike  the  floor  at  the  same 

time  ?    Repeat  the  experiment  several  times,  and  do  not  expect  more 
than  approximate  agreements. 

111.  Projectiles.  —  Every  projectile  is  acted  upon  by  an 
impulsive  force  and  the  force  of  gravity.     The  path  of 
a  projectile  is  a  parabolic  curve,  the  resultant  of  these 
forces. 


FALLING   BODIES. 


113 


(a)  Suppose  a  ball  to  be  thrown  horizontally.  Its  impulsive  force 
will  give  a  uniform  velocity,  and  may  be  represented  by  a  horizontal 
line  divided  into  equal  parts,  the  mag- 
nitude of  each  part  being  equal  to 
that  of  the  velocity.  The  force  of 
gravity  may  be  represented  by  a  ver- 
tical line  divided  into  unequal  parts, 
representing  the  spaces  1,  3,  5,  7,  etc., 
over  which  gravity  would  move  it  in 
successive  seconds.  Constructing  par- 
allelograms of  forces,  we  find  that  at 
the  end  of  the  first  second  the  ball 
will  be  at  A,  at  the  end  of  the  next 
second  at  JB,  at  the  end  of  the  third 
at  C,  at  the  end  of  the  fourth  at  Z>,  etc. 
The  resistance  of  the  air  modifies  the 
nature  of  the  curve  somewhat.  The 
horizontal  distance,  GE,  is  called  the 
range  of  the  projectile. 

CLASSROOM  EXERCISES. 

1.  What  will  be  the  velocity  of  a  body  after  it  has  fallen  4  seconds? 
Solution :  —  v=gt  =  32.16  x  4  =  128.64.  Ans.  128.64  feet. 

2.  A  body  falls  for  several  seconds.     During  one  of  these  seconds 
it  passes  over  530.64  feet.     Which  one  is  it  ? 

Solution :  —  /'  =  ^(2 1  -  1) 

530.64  =  16.08  x  (2 1  -  1) ;  .-.  t  =  17. 

Ans.  17th  second. 

3.  A  body  was  projected  vertically  upward  with  a  velocity  of  96.4£ 
feet.     How  high  did  it  rise  ? 

v      96.48 

g  -32.16  ~6' 

=  16.08  x  9,=  144.72.      Ans.  144.72  feet. 


FIG.  63. 


Salmon:- 


4.  How  far  will  a  body  fall  during  the  third  second  of  its  fall  ? 

5.  How  far  will  a  body  fall  in  10  seconds?  Ans.  1,608  feet. 

6.  How  far  in  1  second?  Ans.  4.02  feet. 

7.  How  far  will  a  body  fall  during  the  first  second  and  a  half  of 
its  fall? 

8 


114  SCHOOL  PHYSICS. 

8.  How  far  in  12|  seconds? 

9.  A  body  passed  over  787.92  feet  during  its  fall.     What  was  the 
time  required?  Ans.  7  seconds. 

10.  What  velocity  did  it  finally  obtain  ? 

11.  A  body  fell  during  15^  seconds.     Give  its  final  velocity. 

12.  In  an  Atwood  machine,  the  weights  carried  by  the  thread  are 
7|  ounces  each.     When  the  "rider,"  which  weighs  one  ounce,  is  in 
position,  what  is  the  acceleration  ? 

13.  A  stone  is  thrown  horizontally  from  the  top  of  a  tower  257.28 
feet  high,  with  a  velocity  of  60  feet  a  second.     Where  will  it  strike 
the  ground?  Ans.  240  feet  from  the  tower. 

14.  When  a  fishing  line  with  a  heavy  sinker  is  thrown  into  a  stream 
with   a  rapid  current,  it   often   is  carried  down  stream  to  the  full 
length  of  the  line,  and  held  suspended  in  the  water.     Draw  a  diagram 
showing  the  forces  acting  on  the  sinker,  and  how  equilibrium  is  se- 
cured.    Neglect  the  buoyancy  of  the  water. 

15.  A  body  is  thrown  directly  upward  with  a  velocity  of  80.4  feet, 
(a)  What  will  be  its  velocity  at  the  end  of  3  seconds,  and  (6)  in  what 
direction  will  it  be  moving  ? 

16.  In  Fig.  63,  what  is  represented  by  the  following  lines:  Fl? 
Fa?  Aa?  Fc?  Ddf 

17.  A  body  falls  357.28  feet  in  4  seconds.     What  was  its  initial 
velocity?  Ans.  25  feet. 

18.  A  ball  thrown  downward  with  a  velocity  of  35  feet  per  second 
reaches  the  earth  in  12|  seconds,     (a)  How  far  has  it  moved,  and  (&) 
what  is  its  final  velocity? 

19.  (a)  How  long  will  a  ball  projected  upward  with  a  velocity  of 
3,216  feet  continue  to  rise?     (6)  What  will  be  its  velocity  at  the  end 
of  the  fourth  second  ?     (c)  At  the  end  of  the  seventh  ? 

20.  A  ball  is  shot  from  a  gun  with  a  horizontal  velocity  of  1,000 
feet,  at  such  an  angle  that  the  highest  point  in  its  flight  is  257.28  feet. 
What  is  its  range?  Ans.  8,000  feet. 
^  21.  A  body  was  projected  vertically  downward  with  a  velocity  of 
10  feet.     It  was  5  seconds  falling.     Required  the  entire  space  passed 
over.  Ans.  452  feet. 

22.  Required  the  final  velocity  of  the  same  body.     Ans.  170.8  feet. 

23.  A  body  was  5  seconds  rolling  down   an  inclined  plane,  and 
passed  over  7  feet  during  the  first  second.     Give  (a)  the  entire  space 
passed  over,  and  (6)  the  final  velocity. 

24.  A  body  rolling  down  an  inclined  plane  has,  at  the  end  of  the 


FALLING   BODIES.  115 

first  second,  a  velocity  of  20  feet,  (a)  What  space  would  it  pass  over 
hi  10  seconds  ?  (&)  If  the  height  of  the  plane  was  800  feet,  what  was 
its  length?  Ans.  (6)  1,286.4  feet. 

25.  A  body  was  projected  vertically  upward,  and  rose  1,302.48  feet. 
Give  (a)  the  time  required  for  its  ascent,  and  (ft)  the  initial  velocity. 

26.  A  body  projected  vertically  downward  has,  at  the  end  of  the 
seventh  second,  a  velocity  of  235.12  feet.     How  many  feet  did  it 
traverse  in  the  first  4  seconds?  Am.  297.28  feet. 

27.  A  body  falls  from  a  certain  height;    3  seconds  after  it  has 
started,  another  body  falls  from  the  height  of  787.92  feet.    From  what 
height  must  the  first  fall  if  both  are  to  reach  the  ground  at  the  same 
instant?  Ans.  1,608  feet. 

28.  A  body  falls  freely  for  6  seconds.     What  is  the  space  traversed 
during  the  last  two  seconds  of  its  fall  ? 

29.  When  a  body  is  thrown  upward,  does  its  velocity  vary  directly 
or  inversely  with  the  number  of  time-units  it  has  been  rising  ? 

30.  See  definition  of  "parabola"  in  the  dictionary.     When  would 
the  curved  line,  FCE  in  Fig.  63,  become  parallel  with  the  vertical 
line,  FG? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Inclined  track;  iron  balls;  pendu- 
lum; electromagnets;  a  voltaic  battery;  turnbuckle;  blade  of  hack- 
saw ;  screws ;  screw-driver ;  needles ;  thread. 

1.  Graduate  to  centimeters  the  edge  of  the  plank  used  in  Experi- 
ment 54,  using  the  part  outside  the  track  that  was  not  graduated  to 
feet.  Elevate  one  end  of  the  plank  as  in  that  experiment. 

On  the  vertical  face  of  a  movable  wooden  support,  and  more  than 
a  meter  from  its  foot,  tack  a  horizontal  strip  of  soft  wood,  the  thick- 
ness of  which  is  not  less  than  the  radius  of  the  iron  ball  mentioned 
below.  Into  the  vertical  face  of  this  strip  press  a  stout  needle  nearly 
to  its  eye.  The  hole  through  the  needle  should  be  vertical.  An  inch 
or  so  above  the  needle  set  a  common  screw.  Fasten  one  end  of  a 
thread  that  will  pass  through  the  eye  of  the  needle,  and  having  a 
length  of  about  110  cm.,  to  a  small  iron  ball.  Pass  the  other  end  of 
the  thread  through  the  eye  of  the  needle,  fasten  it  to  the  screw,  and 
wrap  it  around  the  screw  until  the  center  of  the  ball  hangs  about  a 
meter  below  the  needle. 

Instead  of  using  the  needle  as  above  described,  a  small,  firm  cork 


116  SCHOOL   PHYSICS. 

may  be  fastened  to  the  vertical  face  of  the  strip,  and  a  threaded 
needle  drawn  vertically  through  the  middle  of  the  cork.  The  thread 
may  then  be  fastened  to  the  screw,  although  the  cork  will  probably 
pinch  it  firmly  enough  to  support  the  ball.  Such  cork  supports  are 
easily  provided,  and  convenient  for  quick  adjustment. 

Swing  the  ball  as  a  pendulum,  and  count  the  number  of  times  it 
passes  through  its  arc  in  60  seconds.  If  the  number  of  swings 
exceeds  60,  turn  the  screw  so  as  to  unwind  some  of  the  thread,  and 
increase  the  distance  between  the  ball  and  the  needle,  or  the  under 
side  of  the  cork.  Swing  the  ball  and  count  as  before,  continuing  the 
adjustment  until  the  ball  makes  60  swings  in  60  seconds.  Place  the 
pendulum  so  that  as  it  swings,  and  as  the  ball  rolls  down  the  inclined 
track,  both  may  be  observed  at  the  same  time. 

With  the  assistance  of  a  friend  who  understands  such  things,  fix 
two  electromagnets  that  are  on  the  same  circuit  so  that  their  attrac- 
tion will  hold  an  iron  ball  at  the  upper  end  of  the  inclined  track, 
and  the  iron  pendulum-bob  at  one  end  of  the  arc  through  which  it 
is  to  swing.  Close  the  circuit  of  the  battery,  and  bring  the  two  iron 
balls  into  their  respective  positions,  separated  from  the  magnets 
only  by  bits  of  thin  paper.  The  attraction  of  the  magnets  will  hold 
the  balls,  one  at  the  top  of  the  track,  and  the  other  at  the  end  of 
its  arc. 

Break  the  circuit,  and  the  two  iron  balls  will  be  released  simulta- 
neously. By  trial,  adjust  the  inclination  of  the  track  so  that  the  ball 
will  roll  the  whole  length  in  4  seconds,  as  measured  by  the  swings  of 
the  pendulum.  By  repeated  trials,  verify  the  accuracy  of  the  figures 
in  the  second  and  fourth  columns  of  the  table  given  in  Experiment  54. 

2.  From  the  frame  of  a  small  pulley  running  with  little  friction 
suspend  a  weight  of  about  2  pounds.  Place  the  wheel  of  the  pulley 
so  that  it  will  run  on  a  No.  10  wire  tightly  stretched  between  oppo- 
site sides  of  the  laboratory,  one  end  of  the  wire  being  a  little  higher 
than  the  other.  The  wire  may  be  tightened  with  a  turnbuckle. 
Just  above  the  wire,  and  parallel  with  it,  stretch  a  cord.  From  the 
upper  end  of  the  wire  start  the  pulley  with  its  load,  and  note  the 
point  where  it  is  at  the  end  of  3  seconds.  If  the  distance  traversed 
in  the  3  seconds  is  not  at  least  9  feet,  increase  the  inclination  of  the 
wire.  Mark  the  point  where  the  pulley  is  at  the  end  of  the  third 
second  by  a  strip  of  paper  hung  from  the  cord  so  that  its  lower  end 
will  be  struck  by  the  top  of  the  pulley  as  it  passes.  Mark  the  point 
on  the  cord  above  the  starting  point  of  the  pulley  by  tying  a  thread 


FALLING  BODIES.  117 

there.  Divide  the  intervening  distance  into  9  equal  parts.  Hang 
similar  paper  strips  from  the  cord,  at  distances  of  5  such  equal  parts 
and  of  8  such  equal  parts  above  the  strip  already  hung,  and  of  7  such 
equal  parts  and  16  such  equal  parts  below  it. 

Swing  the  pendulum  that  vibrates  seconds.  As  its  thread  passes  a 
vertical  line  on  the  wooden  support  drawn  downward  f  rom  the  needle, 
start  the  pulley,  and  see  if  it  taps  the 'successive  strips  as  the  pendu- 
lum successively  passes  the  vertical  line.  If  the  weight  carried  by 
the  pulley  is  of  iron,  the  weight  and  the  pendulum-bob  may  be  simul- 
taneously released  as  in  Exercise  1. 

XOTE.  —  A  good  Atwood  machine  is  an  expensive  piece  of  appa- 
ratus, and  unfortunately  many  schools  and  laboratories  have  none. 
If  any  particular  school  'is  thus  equipped,  the  teacher  should  provide 
for  its  use  in  the  verification  of  the  laws  of  falling  bodies,  the  approx- 
imate determination  of  the  acceleration  due  to  gravity,  etc. 

3.  Modify  Experiment  53  by  using  two  iron  balls  of  different  mass 
supported  by  the  attraction  of  two  electromagnets  that  are  in  the 
same  circuit.     Tie  the  magnets  to  a  stick,  and  hold  them  and  the 
magnetically  supported   balls  from  an  upper  window.     When  you 
are  sure  that  the  balls  are  at  the  same  level,  break  the  circuit.    A  co- 
worker  standing   on  the   ground  will   report  whether  the  different 
masses  make  the  journey  in  the  same  time. 

4.  A  ball  is  thrown  horizontally  with  a  velocity  of  20  feet  a  second. 
Using  any  convenient  scale  and  the  cross-section  paper,  map  the  posi- 
tion of  the  ball  at  the  end  of  half  seconds  for  5  seconds.     Bend  the 
thin  blade  of  a  hack-saw  or  other  flexible  bar  so  that  its  edge  will 
pass  through  as  many  of  these  points  as  possible.    Along  the  side  of  the 
blade,  trace  a  pencil  mark  to  represent  the  path  of  the  ball.     See  Ex- 
ercise 11,  p.  95,  and  compare  your  curve  with  Fig.  63.     If  any  point 
thus  located  lies  much  out  of  the  curve,  reexamine  your  work  for 
that  point.     On  your  diagram,  lay  off  and  measure  coordinates  for  the 
point  that  represents  the  position  of  the  ball  at  the  end  of  3.25  seconds 
and  5.5  seconds  from  the  beginning  of  its  fall.     Compare  the  results 
of  your  work  with  corresponding  results  obtained  by  computation.    In 
tracing  the  curve,  run  the  pencil  to  the  lower  end  of  the  saw  blade. 

5.  From  a  rectangular  wooden  block  about  30  x  23  x  4  cm.,  cut 
a  semi-cycloid,  thus  shaping   the  piece  marked  B  in  Fig.  64.     Cut 
a  groove  in  the  curved  edge,  and  fasten  the  block  against  the  black- 
board so  that  its  long   edge  shall  be  vertical.      A  small  ball   that 
has  rolled  down  the  cyeloidal  path  will  be  projected  with   a  con- 


118  SCHOOL.  PHYSICS. 

stant  horizontal  velocity  and  an  accelerated  vertical  velocity.  Let 
one  of  two  pupils  working  together  adjust,  by  repeated  trials,  a  ruler 
so  that  the  projected  ball  will  just  touch  it,  and  thence  determine 
and  mark  the  point  passed  over  by  the  center  of  the  ball.  In  this 
way  determine  the  loci  of  points  sufficiently  numerous  to  plot  on  the 

blackboard  the  path  described  by  the 
center  of  the  projected  ball.  From 
the  center  of  the  ball  at  the  lowest 
point  of  its  cycloidal  path  draw  a 
horizontal  line,  and  mark  oif  a  num- 
ber of  equal  spaces  upon  it.  These 
will  represent  the  horizontal  motions 
of  the  ball  in  equal  intervals  of  time. 
From  each  division  on  this  line,  draw 
a  vertical  line,  /,  to  the  plotted  path, 
and  measure  the  lengths  of  these 
lines.  They  represent  the  spaces 
fallen  in  the  several  intervals  of  time. 
Show  that,  for  each  interval  of  time, 
jrIG  54.  /  =  ktz,  k  being  some  constant.  If 

the  horizontal   intervals    are    made 

equal  to  the  horizontal  speed  of  the  ball  per  second,  k  will  equal  \  g. 
From  the  measurements  made  on  the  blackboard,  plot  the  curve  on 
cross-section  paper. 


V.    THE  PENDULUM. 

112.  A   Simple   Pendulum   is  a  single  material  particle 
supported  by  a  line  without  weight,  and  capable  of  oscil- 
lating   about    a    'fixed    point.       Such    a    pendulum    has 
a    theoretical   but    not   an   actual  existence.       Its  prop- 
erties   may    be    approximately    determined    by    experi- 
menting  with   a   small   lead   ball    suspended    by   a   fine 
thread. 

113.  Motion  of  the  Pendulum.  —  When  the  pendulum  is 
drawn  from  its  vertical  position,  the  force  of  gravity,  MGr, 


THE   PENDULUM. 


119 


FIG.  65. 


is  resolved  into  two  components,  one  of  which,  MC,  pro- 
duces pressure  at  the  point  of  support,  while  the  other, 
MH,  acts  at  right  angles  to  it,  producing  motion  toward  N. 
As  the  pendulum  approaches  iV, 
its  kinetic  energy  increases.  This 
energy  carries  the  weight  beyond 
N  toward  0,  against  the  action  of 
the  continually  increasing  compo- 
nent, OP.  By  the  time  the  pen- 
dulum has  arrived  at  0,  its  kinetic 
energy  has  been  wholly  trans- 
formed into  potential  energy. 
Then  OP  pulls  the  weight  toward 
N  again,  transforming  the  poten- 
tial energy  into  kinetic,  which, 
in  turn,  carries  the  weight  once 
more  toward  M.  Thus  the  pendulum  oscillates  for  an 
indefinite  time  by  the  alternate  action  of  gravity  and  its 
acquired  energy  of  motion. 

114.  Definitions.  —  The  motion  from  one  extremity  of 
the  arc  through  which  a  pendulum  swings  to  the  other  is 
called  an  oscillation.  The  "time  occupied  in  moving  over 
this  arc  is  called  the  time  or  period  of  oscillation.  The 
angle  measured  by  half  this  arc  is  called  the  amplitude  of 
oscillation.  The  trip  from  M  to  0  is  an  oscillation.  The 
angle,  MAN,  is  the  amplitude  of  oscillation. 

(a)  The  motion  from  M  to  0  and  back  again,  one  "  swing-swang," 
is  sometimes  called  a  "  complete  vibration."  The  time  occupied  by  the 
round  trip,  or  in  passing  from  any  point  to  its  next  passage  in  the 
same  direction  through  the  same  point,  is  sometimes  called  a  "  com- 
plete period." 


120 


SCHOOL  PHYSICS. 


Experiment  56.  —  Suspend  three  lead  bullets  and  a  small  iron  ball 
as  shown  in  the  accompanying  figure.  The  lengths  of  the  threads, 
measured  between  the  points  of  support  and  the 
centers  of  the  balls,  should  be  as  1:  |-:  ^;  e.g., 
1  yard,  9  inches,  and  4  inches  respectively. 
Set  one  of  the  pendulums  swinging  through  a 
small  arc,  and  count  the  oscillations  made  in 
10  seconds.  Set  the  same  pendulum  swinging 
through  a  somewhat  larger  arc,  and  count  the 
oscillations  as  before.  Record  and  compare 
results.  Repeat  the  experiments  with  each  of 
the  pendulums,  recording  and  comparing  results 
in  each  case.  Note  the  effect  of  amplitude  or 
of  mass  on  the  period  of  oscillation. 

From  your  notes,  or  by  fresh  experiment, 
determine  the  period  of  each  pendulum,  and 
observe  the  relation  between  the  period  of  oscil- 
lation and  the  length  of  the  pendulum. 

Place  a  magnet  under  the  iron  ball,  so  that 
when  the  latter  swings  it  will  just  clear  the  end 
of  the  magnet.  Swing  the  iron  pendulum,  and 
count  the  number  of  oscillations  made  in  10 

seconds.     The  attraction  of  the  magnet  being  added  to  that  of  the 
earth,  the  acceleration  is  increased  and  the  period  is  lessened. 

115.  Laws  of  the  Pendulum.  —  When  the  amplitude  of 
oscillation  does  not  exceed  three  degrees,  the  period  of 
oscillation  depends  mainly  upon  the  length  of  the  pen- 
dulum and  the  acceleration  due  to  gravity.  Representing 
period  by  £,  and  length  by  I,  the  relation  is  expressed 
by  the  formula 


FIG.  66. 


The  following  laws  are  consistent  with  this  formula  and 
with  the  results  of  numberless  experiments  :  — 

(1)  At  any  given  place,  the  vibrations  of  a  given  pen- 
dulum are  isochronous,  i.e.,  are  made  in  equal  periods. 


THE   PENDULUM.  121 

(2)  The  period  of  oscillation  is  independent  of  the  mate- 
rial or  the  mass  of  the  pendulum. 

(3)  The  period  of  oscillation  varies  directly  as  the  square 
root  of  the  length. 

(4)  The  period  of  oscillation  varies  inversely  as  the  square 
root  of  the  acceleration. 

116.  The  Compound   Pendulum. — Any  pendulum  other 
than  the  simple  or  ideal  pendulum  is  a  compound  pendulum. 
In  its   most  common  form,  it  consists  of  a  slender  rod, 
flexible  at  the  top,  and  carrying  at  the  bottom  a  heavy 
mass  of  metal  known  as  the  bob. 

117.  The   Seconds  Pendulum. — At  any  given  place,  a 
seconds  pendulum  is  one  that  makes  a  single  oscillation  in 
a  second.     At  the  sea-level,  its  length  is  about  39  inches 
at  the  equator  and  about  39.2  inches  near  the  poles.     Its 
value  at   the  sea-level  at  New  York  may  be  found  by 
making  £=1,  and  ^=980.19  cm.,  in  the  formula 


and  solving  the  equation  for  the  value  of  I. 

(a)  The  length  of  the  seconds  pendulum  being  known,  the  length 
of  any  other  pendulum  may  be  found  when  the  period  of  oscillation 
is  given,  or  the  period  of  oscillation  may  be  found  when  the  length 
is  given.  As  the  seconds  pendulum  is  inconveniently  long,  use  is 
often  made  of  one  one-fourth  as  long,  which  oscillates  in  half 
seconds. 

Center  of  Oscillation. 

Experiment  57.  —  Drive  a  small  wire  nail  through  a  flat  board  of 
any  form,  at  some  point  near  its  edge,  as  shown  in  Fig.  67.  Hold 


122 


SCHOOL  PHYSICS. 


the  ends  of  the  wire  by  the  finger  and  thumb,  and  allow  the  board  to 
hang  in  a  vertical  plane.  Fasten  a  small  bullet  to  the  end  of  a  thread, 
and  pass  the  thread  over  the  wire  so  that  the  bullet 
hangs  close  to  the  board.  Move  the  hand  that  sup- 
ports the  wire  horizontally  and  in  the  plane  of  the 
board.  Board  and  bullet  will  swing  as  pendulums. 
If  one  swings  more  rapidly  than  the  other,  lengthen 
or  shorten  the  string  until  they  swing  together. 
With  the  thread  at  this  length,  and  board  and 
bullet  hanging  in  equilibrium,  mark  the  point  on 
the  board  opposite  the  center  of  the  ball.  Holding 
the  board  by  the  wire  as  before,  move  it  with  varied, 
sudden,  and  irregular  motions  in  the  plane  of  the 
board.  The  bullet  will  not  quit  the  marked  place 
on  the  board. 


FIG.  67. 


118.  Centers  of  Suspension  and  Oscillation.  —  In  every 
pendulum  not  simple,  the  parts  near  the  center  of  suspen- 
sion tend  to  move  faster  than  those  further  away,  and 
force  the  latter  to  move  more  rapidly  than  they  other- 
wise would.  Between  these,  there  is  a  particle  that  moves, 
of  its  own  accord,  at  the  rate  forced  upon  the 
others.  This  particle  fulfills  all  the  conditions  of 
a  simple  pendulum  that  has  the  period  of  the 
compound  pendulum.  Its  position  is  called  the 
center  of  oscillation  or  percussion. 


(a)  Fig.  68  represents  a  wooden  bar,  suspended  so  as  to 
have  freedom  of  motion  about  the  point  S,  which  thus  be- 
comes the  center  of  suspension.  G  indicates  the  center  of 
mass,  and  O  the  center  of  oscillation.  S  and  0  are  inter- 
changeable ;  i.e.,  if  the  pendulum  is  suspended  from  its 
center  of  oscillation,  the  period  remains  the  same. 


FIG.  08. 


119.    The  Real  Length  of  a  Pendulum.  —  If  we  consider 
the  length  of  the  compound  pendulum  to  be  the  distance 


THE   PENDULUM. 


128 


between  the  centers  of  suspension  and  oscillation,  all  the 
laws  of  the  simple  pendulum  become  applicable  to  the 
compound  pendulum. 

120.  Uses  of  the  Pendulum.  --  The  continued  motion  of 
a  clock  is  due  to  the  force  of  gravity 
acting  upon  the  weights,  or  to  the  elas- 
ticity of  the  spring.  But  the  weights 
have  a  tendency  toward  positively  accel- 
erated motion,  and  the  spring  toward 
negatively  accelerated  motion.  Either 
defect  would  be  fatal  in  a  timepiece. 
The  properties  of  the  pendulum  set  forth 
in  the  first  law  -enable  us  to  regulate  this 
motion,  and  to  make  it  available  for  the 
desired  end. 

The  pendulum  is  also  used  to  deter- 
mine the  relative  and  absolute  accelera- 
tion of  gravity  at  different  places,  and  in 
this  way  the  figure  of  the  earth.  Having 
at  any  given  place  a  pendulum  of  known 
length,  its  period  may  be  determined  and 
the  value  of  g  computed  from  the  formula 
given  in  §115.  FIQ  69 

(a)  A  pendulum  has  a  strong  tendency  to  maintain  its  plane  of 
oscillation,  a  fact  that  has  been  used  in  the  experimental  demonstra- 
tion of  the  rotation  of  the  earth  upon  its  axis.  The  chief  function  of 
the  wheel-work  of  a  clock  is  to  register  the  number  of  the  vibrations 
of  the  pendulum.  If  the  clock  gains  time,  the  pendulum  is  length- 
ened by  lowering  the  bob ;  if  it  loses  time,  the  pendulum  is  shortened 
by  raising  the  bob. 


124 


SCHOOL   PHYSICS. 


CLASSROOM    EXERCISES. 


No. 

INCHES. 

OSCILLATIONS. 

PERIOD. 

No. 

CM. 

OSCILLATIONS. 

PERIOD. 

1 

9 

20  per  min. 

9 

11 

99.33 

? 

? 

2 

? 

30       " 

9 

12 

9 

9 

2  sec. 

3 

30 

? 

? 

13 

9 

9 

2  min. 

4 

16 

? 

? 

14 

24.83 

? 

9 

5 

? 

9 

|  sec. 

15 

9 

8  per  sec. 

? 

6 

9 

? 

5-  min. 

16 

397.32 

9 

? 

7 

39.37 

?  per  min. 

9 

17 

11.03 

9 

9 

8 

9 

10 

9 

18 

? 

9 

10  sec. 

9 

10 

V  per  sec. 

9 

19 

2,483.25 

9 

9 

10 

9 

1  per  min. 

9 

20 

9 

9 

4  sec. 

21.  How  will  the  periods  of  oscillation  of  two  pendulums  compare, 
their  lengths  being  4  feet  and  49  feet  respectively?  Ans.  As  2  :  7. 

22.  Of  two  pendulums,  one  makes  70  oscillations  a  minute,  the 
other,  80  oscillations  a  minute.      How  do  their  lengths  compare? 

Ans.  As  64  :  49. 

23.  If  one  pendulum  is  4  times  as  long  as  another,  what  are  their 
relative  periods  of  oscillation? 

24.  The  length  of  a  seconds  pendulum  being  39.1  inches,  what 
must  be  the  length  of  a  pendulum  to  oscillate  in  £  second  ? 

25.  How  long  must  a  pendulum  be  to  oscillate  (a)  once  in  8  seconds? 
(b)  In  i  second? 

26.  How  long  must  a  pendulum  be  to  oscillate  once  in  3^  seconds? 

27.  Find  the  length  of  a  pendulum  that  will  oscillate  5  times  in  4 
seconds.  Ans.  25.02  -f  inches. 

28.  A  pendulum  5  feet  long  makes  400  oscillations  during  a  certain 
time.  ,  How  many  oscillations  will  it  make  in  the  same  time  after  the 
pendulum  rod  has  expanded  0.1  of  an  inch? 

29.  At  Paris,  g  =  981  cm.     Determine  the  length  of  the  seconds 
pendulum  at  that  place. 

30.  A  lead  ball  is  suspended  as  a  pendulum.     From  the  center  of 
the  ball  it  is  83  inches  to  its  center  of  suspension.     The  pendulum 
oscillates  206  times  in  5  minutes.     From  the  formula  given  in  §  115, 
determine  the  acceleration  due  to  gravity  at  the  time  and  place  of  the 
experiment.  Ans.  32.188  feet. 


THE   PENDULUM.  125 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Wooden  bars,  etc.,  for  pendulums;  a 
pendulum-clock ;  a  piece  of  sheet  iron ;  mercury ;  a  telegraph  sounder 
or  an  electric  bell. 

1.  Set  up  a  pendulum  of  length  as  great  as  you  can  conveniently. 
Set  up  another  that  oscillates  just  twice  as  often  in  a  given  time. 
Determine  the  ratio  between  the  lengths  of  the  two  pendulums. 
Shorten  the  shorter  pendulum  until  it  oscillates  three  times  as  fast 
as  the  other.  Determine  the  relative  lengths  as  before.  Shorten  the 
shorter  pendulum  again  until  it  oscillates  four  times  as  fast,  and  find 
the  ratio  as  before.  In  your  notebook,  record  the  data  obtained,  using 
the  following  form,  and  placing  the  ascertained  ratios  in  the  places  of 
x,  y,  and  z :  — 

Relative  Numbers  Relative 

of  Oscillations.  Lengths. 

1 .1 

2 x 

3 y 

4 z 

5 ? 

6  * 


Can  you  see  any  law  or  rule  governing  in  such  cases?  Try,  with- 
out experiment,  to  put  the  proper  figures  in  the  places  of  the  two 
interrogation  points. 

2.  Set  up  the  pendulum  used  in  Exercise  1,  p.  115,  or  a  similar 
one,  and   adjust  its  length  so  that  it  will  oscillate  60  times  in  60 
seconds.     The  eye  of  the  needle  should  be  not  much  larger  than  is 
necessary  for  the  thread  used.     Measure  the  distance  from  the  center 
of  the  bob  to  the  needle.     From  the  data  thus  secured,  compute  the 
value  of  g. 

3.  Set  up  a  similar  pendulum,  but  with  a  shorter  thread.     Adjust 
the  length  of  the  pendulum  by  turning  the  screw  until  the  pendu- 
lum oscillates  60  times  in  30  seconds.      Measure  the  length  of  the 
pendulum.     Compare  its  period  with  that  of  the  one  used  in  Exer- 
cise 2.     Compare  its  length  with  that  of  the  one  used  in  Exercise  ?. 
How  do    these    comparisons    tally    with    the    statement    made    in 
§  115  (3) ? 


126  SCHOOL   PHYSICS. 

4.  Shorten  the  thread  of  the  pendulum  used  in  Exercise  3  until 
the  pendulum  oscillates  60  times  in  20  seconds.     Measure  the  length 
of  the  pendulum.     Compare  its  period  with  that  of  those  used  in 
Exercises  2  and  3.      Compare  its  length  with  the  lengths  of  those. 
How  do  these  results  conform  to  the  law  referred  to  above  ? 

5.  Using  these  pendulums  successively,  test  the  accuracy  of  the 
law  given  in  §  115  (1). 

6.  Using   either   of   these   pendulums  and   another   prepared  by 
you  for  that  purpose,  test  the  accuracy  of  the  second  law  given  in 
§  115. 

7.  On  a  stout  thread,  fasten  5  or  6  lead  bullets  at  successive  inter- 
vals of  10  cm.,  and  suspend  the  combination  as  a  pendulum.     Swing 
it  as  a  pendulum.     Does  the  string  retain  its  rectilinear  form  while 
the  compound  pendulum  is  oscillating?     Account  for  any  observed 
difference  in  this  respect  between  this  pendulum  and  those  previously 
used. 

8.  Through  the  laboratory  meter  stick  or  a  similar  strip  of  wood, 
drill  or  burn  a  small  hole  3  cm.  from  one  end.     Using  this  as  a  center 
of  suspension,  locate  the  center  of  oscillation.      Determine  the  real 
length  of  the  meter-stick  pendulum.     Suspend  a  bullet  by  a  single 
thread,  and  adjust  its  length  so  that  it  will  swing  with  the  same 
period  as  the  meter-stick  pendulum.      Compare  the  length  of  this 
pendulum  with  the  distance  between  the  centers  of  suspension  and 
oscillation  of  the  other  pendulum. 

9.  Remove  the  dial  of  a  clock,  and  study  the  movements  of  the 
escapement  (mn  in  Fig.  69),  and  of  the  escapement  wheel,  R.     What 
does  it  enable  the  lifted  weights  or  the  coiled  spring  of  the  clock 
to  do  to  the  pendulum  ?     What  does  it  enable  the  pendulum  to  do  to 
the  weights  or  the  spring?    What  would  happen  to  the  weights  or 
to  the  spring  if  the  escapement  should  be  suddenly  removed?    What 
would  happen  to  the  pendulum  if  the  escapement  should  be  removed? 
How  many  times  must  the  pendulum  oscillate  that  the  escapement 
wheel  may  turn  around  once  ? 

10.  Suspend  a^heavy  metallic  ball  by  two  fine  wires  that  are  gripped 
at  the  lower  horizontal  edge  of  a  metallic  clamp.     To  the  bottom  of 
the  ball,  solder  a  short  pointed  iron  or  platinum  wire.     (See  Fig.  44.) 
Make  a  slight  depression  in  a  small  plate  of  sheet  iron,  and  solder 
a  small  copper  wire  to  the  plate.     Fasten  the  plate  beneath  the  pen- 
dulum bob  so  that  the  wire  pointer  will  just  touch  a  drop  of  mer- 
cury placed  in  the  depression  in  the  plate.      The  mercury  globule 


SIMPLE   MACHINES.  127 

should  be  so  placed  that  when  the  pendulum  swings,  its  pointer  shall, 
at  each  oscillation,  touch  the  mercury,  but  not  the  plate.  Connect 
the  wire  that  is  soldered  to  the  plate  with  one  pole  of  a  voltaic  cell 
or  battery.  Connect  the  other  pole  of  the  battery  through  a  tele- 
graph sounder  or  single-stroke  electric  bell  with  the  end  of  the  pendu- 
lum wire  where  it  protrudes  above  the  supporting  clamp.  Swing  the 
pendulum.  As  the  pointer  passes  through  the  mercury,  it  will  "  close 
the  circuit "  of  the  battery,  and  the  sounder  will  click  or  the  bell 
will  strike.  Adjust  the  length  of  the  pendulum  until  it  gives  60  sig- 
nals in  60  seconds.  Make  this  pendulum  a  permanent  feature  of  the 
laboratory. 

11.  From  a  board,  cut  two  isosceles-triangular  pieces  with  sides  of 
4  and  24  inches.  Insert  a  small  screw-eye  at  the  pointed  end  of  one, 
and  another  screw-eye  at  the  middle  of  the  4-inch  side  of  the  other. 
Suspend  the  wooden  pieces  by  the  screw-eyes,  and  swing  them  as  pen- 
dulums. Determine  the  period  of  each,  and  thence  compute  the  real 
lengths  of  the  two  pendulums. 


VI.    SIMPLE   MACHINES. 

121.  Machines.  —  In    mechanics,    the   word    "  machine  " 
signifies  an  instrument  for  the 

conversion  of  motion  or  the 
transference  of  energy.  Thus, 
a  machine  may  be  designed 
to  convert  rapid  motion  into 
slow  motion ;  e.g.,  a  crowbar. 
There  are  six  simple  ma-  FlG-  70- 

chines,  —  the  lever,  the  wheel  and  axle,  the  pulley,  the  in- 
clined plane,  the  wedge,  and  the  screw. 

122.  Weight   and   Power.  —  The   action   of   a   machine 
involves   two   forces,   the   weight   and   the   power.     The 


128  SCHOOL   PHYSICS. 

power  signifies  the  magnitude  of  the  force  that  acts  upon  one 
part  of  the  machine  ;  the  weight  signifies  the  magnitude  of 
the  force  exerted  by  another  part  of  the  machine  upon  some 
external  resistance.  The  general  problem  relating  to  ma- 
chines is  to  find  the  ratio  between  power  and  weight ; 
i.e.,  to  determine  the  " mechanical  advantage"  of  the 
machine. 

(a)  It  is  common  in  elementary  discussions  to  neglect  friction, 
and  to  assume  that  the  parts  of  the  machine  are  perfectly  rigid  and 
without  weight. 

123.  A  Machine   cannot   Create  Energy.  —  No  machine 
can  create  or  increase  energy.    In  fact,  the  use  of  a  machine 
is  accompanied  by  a  waste  of  the  energy  that  is  needed  to 
overcome  the  resistances  of  friction,  the  air,  etc.     A  part 
of  the  energy  exerted  must,  therefore,  be  used  upon  the 
machine  itself,  thus  diminishing  the  amount  that  can  be 
transmitted  or  utilized  for  doing  the  work  in  hand. 

124.  General  Laws  of  Machines.  —  The  operations  of  a 
machine  are  subject  to  the  principles  of  "  the  conservation 
of  energy ;  "  the  work  done  by  the  power  equals  the  work 
done  on  the  weight. 

(1)  The  power  multiplied  by  the  distance  through  which  it 
moves  equals  the  weight  multiplied  by  the  distance  through 
which  it  moves:  Pl  =  Wl'. 

(2)  The  power  multiplied  by  its  velocity  equals  the  weight 
multiplied  by  its  velocity :  Pv=  Wv' . 

125.  Efficiency  of  Machines.  —  As  was  hinted  in  §  123, 
part  of  the  work  done  upon  a  machine  is  expended  in  over- 
coming resistances  that  correspond  to  waste,  —  resistances 


SIMPLE   MACHINES.  129 

other  than  that  which  the  machine  was  designed  to  over- 
come, .such  as  friction,  etc.  The  ratio  that  the  useful  work 
done  by  the  machine  bears  to  the  total  work  done  on  the 
machine  is  called  the  efficiency  of  the  machine.  If  this  ratio 
could  be  brought  up  to  unity,  we  should  have  a  perfect 
machine,  —  the  impossible  thing  that  would  supply  "  per- 
petual motion." 

(a)  Whenever  we  find  that  a  machine  does  less  work  than  was 
done  upon  it,  we  should  bear  in  mind  that  the  missing  energy  has 
not  been  destroyed.  Mechanical  energy  has  been  transformed  into 
a  familiar  form  of  molecular  energy,  and  exists  somewhere  in  the  form 
of  heat. 

126.  Impediments    to    Motion.  —  The    impediments    to 
motion  most  frequently  met  in  the  use  of  machines  result 
from  rigidity  or  from  friction.     The  first  of  these  is  fa- 
miliarly illustrated  in  the  stiffness  of  a  pulley  rope.     The 
second  will  receive  further  consideration  in  the  following 
paragraph,     Due  allowance  must  be  made  for  these  hin- 
drances in  all  close  calculations  of  the  useful  work  of  any 
machine.     If  the  machine  is  designed  merely  to  support 
a  load,  the  greater  the  impediments,  the  less  the  power 
required ;    if   the   machine   is  designed  to  move  a  load, 
the  greater  the  impediments,  the  greater  the  power  re- 
quired. 

127.  Friction    is    the    resistance    that    a    moving   body 
meets  from   the    surface   on   ivhich  it  moves,   and  may  be 
rolling  or  sliding.     It  is  due  partly  to  the   adhesion   of 
bodies,  but   more   largely   to  their   roughness.     Friction 
proper  is  independent  of  the  velocity  of  the  motion  and  of 
the  area  of  contact.    It  depends  upon  the  nature  of  the  two 
surfaces  and  upon  the  pressure   upon  them,  and  varies 


130 


SCHOOL   PHYSICS. 


FIG.  71. 


directly  as  such  pressure.      The    quotient    arising  from 
dividing  the  force  necessary  to  keep  the  body  in  motion 

by  the  normal  pressure 
that  the  body  exerts  on 
the  surface  over  which  it 
moves,  i.e.,  the  ratio  be- 
tween the  friction  and  the 
pressure,  is  called  the  co- 
efficient of  friction. 

(a)  Friction  is  generally  lessened  by  polishing  and  lubricating  the 
surfaces  that  move  upon  each  other,  and  often  by  making  the  two 
bodies  of  different  material.  The  axles  of  railway  cars  are  made  of 
steel,  the  boxes  in  which  they  turn  are  made  of  brass,  the  surfaces  are 
made  smooth  and  kept  oiled.  In  spite  of  all  these  precautions,  the 
axle  often  becomes  heated  by  friction  to  such  an  extent  as  to  render 
it  necessary  to  stop  the  train. 

128.  A  Lever  is  an  inflexible  bar  freely  movable  about  a 
fixed  axis  called  the  fulcrum.  Every  lever  is  said  to  have 
two  arms.  The  power  arm  is  the  perpendicular  distance 
from  the  fulcrum  to  the  line  in  which  the  power  acts  ;  the 
weight  arm  is  the  perpendicular  distance  from  the  ful- 
crum to  the  line  in  which  the  weight  acts.  If  the  arms 
are  not  in  the  same  straight  line,  the  lever  is  called  a 
bent  lever. 

(a)  There  are  three  classes  of  levers,  depending  upon  the  relative 
positions  of  power,  weight,  and  fulcrum. 


Fia.  72. 
(1)  If  the  fulcrum  is  between  the  power  and  weight  (PFW),  the 


SIMPLE   MACHINES. 


131 


lever  is  of  the  first  class  (Fig.  72)  ;  e.g.,  crowbar,  balance,  steelyard, 
scissors,  pincers. 

(2)  If  the  weight  is  between  the  power  and  the  fulcrum  (P  WF), 
the    lever    is    of   the   second    class 

(Fig.  73);   e.g.,   cork-squeezer,   nut- 
cracker,  wheelbarrow.  ^r 

(3)  If  the  power  is  between  the      p 
weight  and   the    fulcrum   (WPF), 
the    lever    is    of    the    third    class 
(Fig.  74) ;    e.g.,    fire-tongs,    sheep- 
shears. 


FIG.  74. 


FIG.  75. 


(b)  In  the   bent  lever,  represented  in  Fig.   75,  and  acted  upon 

by  two  forces  not  par- 
allel, the  arms  are  not 
FP'and  FW,butFP 
and  FW. 

129.  Mechanical 
Advantage  of  the 
Lever.  —  The  gen- 
eral laws  of  machines  may  be  adapted  to  the  lever  as 
follows  :  A  given  power  will  support  a  weight  as  many  times 
as  great  as  itself  as  the  power  arm  is  times  as  long  as  the 
weight  arm. 

(a)  The  ratio  between  the  arms  of  the  lever  will  be  the  same  as  the 
ratio  between  the  velocities  of  the  power  and  the  weight,  and  the  same 
as  the  ratio  between  the  distances  moved  by  the  power  and  the  weight. 
If  the  power  arm  is  twice  as  long  as  the  weight  arm,  the  power  will 
move  twice  as  fast  and  twice  as  far  as  the  weight  does.  The  power 
and  weight  are  inversely  proportional  to  the  corresponding  arms  of 
the  lever : 

P:  W::WF:I>F. 

The  power  multiplied  by  the  power  arm  equals  the  weight  multi- 
plied by  the  weight  arm : 

P  x  PF  =  W  x  WF. 

NOTE.  —  In  all  experimental  work,  the  lever  should  be  loaded  so  as 
to  be  in  equilibrium  before  the  power  and  weight  are  applied.  It  is 


132  SCHOOL   PHYSICS. 

to  be  noticed  that,  when  we  speak  of  the  power  multiplied  by  the 
power  arm,  we  refer  to  the  abstract  numbers  representing  the  power 
and  power  arm.  We  cannot  multiply  pounds  by  feet,  but  we  can 
multiply  the  number  of  pounds  by  the  number  of  feet. 

130.  The  Moment  of  a   Force   with  respect  to  a  given 
point  is  its  tendency  to  produce  rotation   about  that  point, 
and  is  measured  by  the  product  of  the  numbers  represent- 
ing respectively  the  magnitude  of  the  force  and  the  perpen- 
dicular distance  between  the  given  point  and  the  line  of  the 
force. 

(a)  In  the  case  of  the  lever  represented  in  Fig.  72,  the  weight  arm 
is  8  mm.,  and  the  power  arm  is  30  mm.  Suppose  that  the  power  is 
4  grams  and  represent  the  weight  by  x.  Then  the  moment  of  the 
force  acting  on  the  power  arm  will  be  represented  by  (4  x  30  =)  120, 
•and  the  moment  of  the  force  acting  on  the  weight  arm  by  8  a:. 

131.  Moments  Applied  to  the  Lever.  — Sometimes  several 
forces  act  upon  one  or  both  arms  of  a  lever,  in  the  same 

1V  or  in  opposite  direc- 

tions.     Under    such 


& 
20 1 — Jg r — s r £0 1 30    circumstances,      the 

c\  d\  «  /        Zever  m7£  50  in  equi- 

i%  s  2^  ifc      librium  when  the  sum 

of  the  moments  of  the 

forces  tending  to  turn  the  lever  in  one  direction  is  equal  to 
the  sum  of  the  moments  of  the  forces  tending  to  turn  the 
lever  in  the  other  direction.  Representing  the  moments 
of  the  several  forces  acting  upon  the  lever  represented 
in  the  figure  by  their  respective  letters  and  numerical 
values, 


b+c+d=a+e+f 


or  c  +  d  —  a  =  e-\-f—  b. 


30  +  30+40  =  30  +  25+45. 
30  +  40-30  =  25  +  45-30. 


SIMPLE   MACHINES. 


133 


132.  The  Balance  is  essentially  a  lever  of  the  first  class, 
having  equal  arms.  The  beam  carries  a  pan  at  each  end,  — 
one  for  the  weights 
used,  the  other  for  the 
article  to  be  weighed. 

(a)  Dishonest  dealers  some- 
times use  balances  with  arms 
of  unequal  lengths.  When 
buying,  they  place  the  goods 
on  the  shorter  arm ;  when 
selling,  on  the  longer.  The 
cheat  may  be  exposed  by 
changing  the  goods  and 
weights  to  the  opposite  sides 

of  the  balance.  The  true  weight  may  be  found  by  weighing  the 
article  first  on  one  side  and  then  on  the  other,  and  taking  the  geo- 
metrical mean  of  the  t\vo  false  weights ;  that  is,  by  finding  the  square 
root  of  the  product  of  the  two  false  weights. 

(6)  The  true  weight  of  a  body  may  be  found  with  a  false  balance 
in  another  way.  Place  the  article  to  be  weighed  in  one  pan,  and 
counterpoise  it,  as  with  shot  or  sand  placed  in  the  other  pan.  Remove 
the  article,  and  place  known  weights  in  the  pan  until  they  balance  the 
shot  or  sand  in  the  other  pan.  These  known  weights  will  represent 
the  true  weight  of  the  article  in  question. 


133. 


Compound  Lever.  — Sometimes  it  is  not  convenient 
to  use  a  lever  sufficiently  long  to 
make  a  given  power  support  a  given 
weight.  A  combination  of  levers, 
called  a  compound  lever,  may  then 
be  used.  Hay  scales  may  be  men- 
tioned as  a  familiar  illustration 
of  the  compound  lever.  In  this 
case  we  have  the  following  statical 

FIG.  78.  law  :  — 


134  SCHOOL  PHYSICS. 

The  continued  product  of  the  power  and  the  lengths  of  the 
alternate  arms,  beginning  with  the  power  arm,  equals  the 
continued  product  of  the  weight  and  the  lengths  of  the  alter- 
nate arms,  beginning  with  the  weight  arm. 

CLASSROOM  EXERCISES. 

1.  If  a  power  of  50   pounds  acting  upon  any  kind  of  machine 
moves  15  feet,  («)  how  far  can  it  move  a  weight  of  250  pounds? 
(b)  How  great  a  load  can  it  move  75  feet? 

2.  If  a  power  of  100  pounds  acting  upon  a  machine  moves  with 
a  velocity  of  10  feet  per  second,  (a)  to  how  great  a  load  can  it  give  a 
velocity  of  125  feet  per  second?     (6)  With  what  velocity  can  it  move 
a  load  of  200  pounds  ? 

3.  A  lever  is  10  feet  long  with  its  fulcrum  in  the  middle.    A  power 
of  50  pounds  is  applied  at  one  end.    (a)  How  great  a  load  at  the  other 
end  can  it  support?     (6)  How  great  a  load  can  it  lift? 

Ans.  (b)  Anything  less  than  50  pounds. 

4.  The  power  arm  of  a  lever  is  10  feet.     The  weight  arm  is  5  feet, 
(a)  How  long  will  the  lever  be  if  it  is  of  the  first  class?     (6)  If  it  is 
of  the  second  class?     (c)  If  it  is  of  the  third  class? 

5.  A  bar  12  feet  long  is  to  be  used  as  a  lever,  keeping  the  weight 
3  feet  from  the  fulcrum,     (a)  What  class  or  classes  of  levers  may  it 
represent?     (b)  What  weight  can  a  power  of  10  pounds  support  in 
each  case  ? 

6.  The  length  of  a  lever  is  10  feet.     Four  feet  from  the  fulcrum 
and  at  the  end  of  that  arm  is  a  weight  of  40  pounds ;  two  feet  from 
the  fulcrum,  on  the  same  side,  is  a  weight  of  1,000  pounds.     What 
force  at  the  other  end  will  counterbalance  both  weights? 

Ans.  360  pounds. 

7.  At  the  opposite  ends  of  a  lever  20  feet  long,  two  forces  are  act- 
ing whose  sum  is  1,200  pounds.     The  lengths  of  the  lever  arms  are  as 
2  to  3.     What  are  the  two  forces  when  the  lever  is  in  equilibrium? 

8.  The  length  of  a  lever  is  8  feet,  and  its  fulcrum  is  in  the  center. 
A  force  of  10  pounds  acts  at  one  end ;  1  foot  from  it  is  another  of 
100  pounds ;  3  feet  from  the  other  end  is  a  force  of  100  pounds.     The 
direction  of  all  the  forces  is  downward.     Where  must  a  downward 
force  of  80  pounds  be  applied  to  balance  the  lever  ? 

Ans.  3  feet  from  the  fulcrum. 


SIMPLE    MACHINES.  135 

9.  The  length  of  a  lever,  ab,  is  6£  feet.     The  fulcrum  is  at  c.     A 
downward  -  force  of  60  pounds  acts  at  a ;  one  of  75  pounds,  at  a 
point,  d,  between  a  and  c,  2|-  feet  from  the  fulcrum.     Required  the 
amount  of  equilibrating  force  acting  at  6,  the  distance  between  b  and 
c  being  f  of  a  foot. 

10.  On  a  lever,  ab,  a  downward  force  of  40  pounds  acts  at  a,  10 
feet  from  fulcrum,  c;  on  the  same  side,  and  6|  feet  from  c,  a  56-pound 
force,  d,  acts  upward.     The  distance,  6c,  is  3  feet.     A  downward  force 
of  96  pounds  acts  at  b.     (a)    Where  must  a  fourth   force  of  28 
pounds  be  applied  to  balance  the  lever,  and  (6)  what  direction  must 
it  have  ? 

11.  A  beam  18  feet  long  is  supported  at  both  ends.     A  weight  of  1 
ton  is  suspended  3  feet  from  one  end,  and  a  weight  of  14  hundred- 
weight 8  feet  from  the  other  end.     Give  the  pressure  on  each  point  of 
support.  Ans.  2,288|  pounds  at  one  end. 

12.  The  length  of  a  lever  is  3  feet.     Where  must  the  fulcrum  be 
placed  so  that  a  weight  of  200  pounds  at  one  end  shall  be  balanced 
by  40  pounds  at  the  other  end  ? 

13.  In  one  pan  of  a  false  balance,  a  roll  of  butter  weighs  1  pound 
9  ounces ;  in  the  other,  2  pounds  4  ounces.     Find  the  true  weight. 

14.  A  and  B,  at  opposite  ends  of  a  bar  6  feet  long,  carry  a  weight 
of  300  pounds  suspended  between  them.     A's  strength  being  twice  as 
great  as  B's,  where  should  the  weight  be  hung? 

15.  A  and  B  carry  a  quarter  of  beef  weighing  450  pounds  on  a  rod 
between  them.     A's  strength  is  1|  times  that  of  B's.    The  rod  is  8  feet 
long.    Where  should  the  beef  be  suspended? 

16.  The  length  of  a  lever  is  16  feet.    At  one  end  is  a  weight  of  100 
pounds.     What  power  applied  at  the  other  end,  3^  feet  from  the  ful- 
crum, is  required  to  move  the  weight? 

17.  A  power  of  50  pounds  acts  upon  the  long  arm  of  a  lever  of  the 
first  class.     The  arms  of  this  lever  are  5  and  40  inches  respectively. 
The  other  end  acts  upon  the  long  arm  of  a  lever  of  the  second  class. 
The  arms  of  this  lever  are  6  and  33  inches  respectively,     (n)  Figure 
the  machine,     (b)  Find  the  weight  that  may  be  thus  supported, 
(c)  What  power  will  support  a  weight  of  4,400  kilograms? 

18.  A  uniform  bar  of  metal  10  inches  long  weighs  4  pounds.     A 
weight  of  6  pounds  is  hung  from  one  end  of  the  bar.     Determine  the 
position  of  the  fulcrum  upon  which  the  loaded  bar  will  balance. 


136 


SCHOOL  PHYSICS. 


FIG.  70. 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  handful  of  wheat;  weights  made  of 
bags  containing  sand ;  a  tin  can  of  known  weight  to  serve  as  a  scale- 
pan  ;  wooden  bars,  blocks;  and  board  as  described  below ;  plumbago 
powder;  a  stout  coverless  dry-goods  box  to  replace  the  frame  shown 
in  Fig.  81,  and  a  wooden  cylinder  about  8  inches  in  diameter  and 
long  enough  to  reach  across  the  box  from  side  to  side. 

1.  Weigh  five  samples  of  wheat,  each  containing  20  grains.  Deter- 
mine the  wreight  of  the  average  grain  of  wheat  and  the  number 

of  such  grains  of 
wheat  in  a  bushel  of 
60  pounds. 

2.  Support  a 
wooden  bar,  prefera- 
bly graduated  (the 
yardstick  or  the  meter 
rod  will  answer  ad- 
mirably), by  a  pin  and 
clevis  at  the  middle  of 
its  length,  as  shown  in 
Fig.  79.  Put  the  bar  in  equilibrium  (as  in  all  such  experimental 
cases),  and  provide  stops  2  or  3  inches  below  each  end  of  the  bar 
to  limit  its  oscillations.  Support 
equal  and  known  weights  by  thread 
loops  at  equal  distances  from  the 
middle  of  the  lever,  and  compare 
the  reading  of  the  dynamometer 
with  the  sum  of  the  suspended 
weights.  Do  they  agree  ?  If  not, 
why  not  ?  Make  the  necessary  cor- 
rection. 

3.  Modify  the  apparatus  used 
in  Exercise  2  by  removing  the 
dynamometer  and  adding  a  coun- 
terpoise, as  shown  in  Fig.  80.  Re- 
place the  weight  at  A  with  one 
twice  as  heavy,  and  shift  its  position  until  the  bar  is  in  equilibrium. 
Note  the  distances  of  C  and  B  from  0.  Using  either  form  of  ap- 
paratus, load  the  two  arms  of  the  lever  with  weights  of  varying  ratios, 


FIG.  80. 


SIMPLE  MACHINES.  137 

and  note  the  agreement  or  disagreement  of  your  results  with  the  sev- 
eral statements  made  in  §§  129  and  131. 

4.  Provide  two  additional  fixed  pulleys  and  use  the  apparatus  in  an 
experimental  verification  of  the  equations  given  in  §  131. 

5.  Take  two  points  at  slightly  different  distances  from  0,  the  ful- 
crum of  the  balance-beam.     Suspend  an  unknown  weight  from  one  of 
these  points,  and  counterpoise  it  with  known  weights  at  the  other  point 
so  taken.    Verify  the  statements  made  in  §  132  (a). 

6.  From  one  of  the  points  taken  as  directed  in  Exercise  5,  sus- 
pend a  tin  can,  and  put  the  lever  in  equilibrium.     From  the  other 
of  those  two  points,  suspend  a  body  of  unknown  weight,  and  find 
its  true  weight  by  the  process  of  double  weighing,  as  described  in 
§  132  (&). 

7.  Get  a  board  4  or  5  feet  long  and  about  1  foot  wide ;  also  a 
wooden  block  about  2x4x8  inches.  Plane  the  board  on  one  side, 
and  the  block  on  one  of  its  2  x  8  inch  and  on  one  of  its  4  x  8  inch 
faces.  Insert  a  small  screw-eye  or  screw-hook  at  the  middle  of  one 
of  its  2x4  inch  faces.  Weigh  the  block.  Attach  a  cord  to  the  screw- 
eye  so  that  the  block  may  be  drawn  lengthwise  on  the  board,  the 
other  end  of  the  cord  being  attached  to  a  spring-balance  or  to  a  scale- 
pan,  as  shown  in  Fig.  71.  Place  the  board  horizontal,  with  its  rough 
surface  up.  Place  the  2x8  inch  rough  surface  of  the  block  on  the 
board,  and  draw  the  block,  using  the  spring-balance  or  sufficient 
weights,  and  keeping  the  cord  horizontal.  Ascertain  what  force  is 
necessary  to  start  the  load.  Determine  the  force  that  will  just  main- 
tain the  sliding  motion  while  you  keep  tapping  on  the  table.  Deter- 
mine the  coefficient  of  friction  for  these  two  surfaces.  Find  the 
averages  of  several  tests. 

Place  the  block  upon  its  4x8  inch  rough  surface,  and  repeat  the 
work.  How  does  the  coefficient  of  friction  now  compare  with  that 
obtained  in  the  first  set  of  tests  ? 

Turn  the  board  over,  and  place  the  2x8  inch  smooth  face  of  the 
block  upon  it.  Make  a  similar  set  of  tests. 

Place  the  block  on  its  4x8  inch  smooth  face,  and  make  another  set 
of  tests.  How  does  the  coefficient  obtained  in  the  last  set  of  tests  com- 
pare with  that  of  the  third  set  ?  How  do  the  coefficients  of  the  third 
and  fourth  sets  compare  with  those  of  the  first  and  second  sets? 

Repeat  the  third  and  fourth  sets  of  tests  with  weights  on  the  blocks 
so  that  the  load  moved  shall  be  successively  2,  3,  and  4  times  the 
weight  of  the  block. 


138  SCHOOL  PHYSICS. 

Smear  the  smooth  surfaces  of  the  board  and  the  block  with  pow- 
dered graphite  or  plumbago,  such  as  is  sold  for  chains  of  bicycles, 
and  repeat  the  tests  with  the  heavier  loads  previously  used. 

Record  all  of  the  conclusions  that  you  draw  from  this  series  of 
experiments. 

8.  Place  the  block  with  its  broad  and  smooth  face  upon  two  round 
lead  pencils  that  lie  parallel  upon  the  smooth  face  of   the  board. 
Determine  the  coefficient  of  rolling  friction,  and  compare  it  with  the 
coefficient  of  sliding  friction  for  the  same  surfaces. 

9.  Wind  the  draw-cord  several  times  around  a  cylinder,  and  arrange 
apparatus  as  shown  in  Fig.  81.     Load  the  cylinder  with  four  equal 

weights  carried  on  cords,  so  that 
the  weight  of  the  cylinder  and 
its  load  shall  equal  the  weight 
of  the  block  and  some  one  of  its 
loads  as  used  in  Exercise  7. 
Determine  the  coefficient  of  roll- 
ing friction,  and  compare  it  with 

that  obtained  for  sliding  friction 
FIG.  81.  i  i 

under  an  equal  pressure. 

10.  Prepare  a  slightly  tapering  pine  rod  about  15  inches  long  and 
about  1  inch  square  at  the  larger  end.     Balance  it  upon  a  knife-edge  or 
other  sharp  support  to  determine  the  distance  of  the  center  of  mass 
from  the- ends  of  the  rod.     The  block  marked  A  in  Fig.  17  will  answer 
as  a  fulcrum  for  this  and  the  other  purposes  of  this  exercise.    Indicate 
the  line  of  support  by  a  pencil  mark  across  the  rod.     Weigh  the  rod 
accurately.     Half  an  inch  from  the  heavy  end  of  the  rod,  suspend  by  a 
thread  loop  a  weight  of  20  grams,  and  so  adjust  the  fulcrum  that  the 
lever  thus  loaded  will  balance.    In  all  such  cases,  see  that  the  fulcrum- 
edge  is  exactly  crosswise  the  length  of  the  lever.    Measure  the  dis- 
tances between  the  fulcrum  and  the  weight,  and  the  fulcrum  and  the 
center  of  mass.     Determine  the  moment  of  the  20  grams  and  of  the 
weight  of  the  lever,  and  see  how  the  two  compare.     Shift  the  position 
of  the  20  grains  weight,  and  repeat  the  work.     Increase  the  suspended 
weight  to  25  or  30  grams,  and  repeat  the  previous  tests.     Record  your 
conclusions. 

11.  Suspend  a  weight  of  100  grams  5  centimeters  from  one  end  of 
a  meter  bar,  and  a  weight  of  500  grams  5  centimeters  from  the  other 
end.     Find  the  point  from  which  the  bar  thus  loaded  must  be  sus- 
pended in   order   that  the  "  system  "  may  just  balance.     From  the 


SIMPLE  MACHINES. 


139 


principles  of  §§  94  and  131,  calculate  the  weight  of  the  meter  bar. 
Verify  the  result  by  actual  weighing. 

134.    The  Wheel  and  Axle  consists  of  a  wheel  united  to 
a  cylinder  in  such  a  way  that  they  may  turn  together  on  a 
common    axis.     It 
is  a  modified  lever 
of     the     first     or 
second   class. 

(a)  Considered  as  a 
lever,   the  fulcrum  is 
FlG  82  at  the  common   axis, 

while  the  arms  of  the 

lever  are  the  radii  of  the  wheel  and  of  the 
axle.     The  usual  arrangement  is  to  take  ac, 
the  radius  of  the  wheel,  as  the  power  arm,  and 
axle,  as  the  weight  arm. 


FIG.  83. 


,  the  radius  of  the 


135.  Mechanical  Advantage  of  the  Wheel  and  Axle.  — 
Evidently,  what  was  said  concerning  the  advantage  of 
the  lever  is  equally  ap- 
plicable here  :  — 


or 


P  :  W::  W  F  :  PF, 
P:  W'.'.r-.R, 

the  radii  of  the  wheel 
and  of  the  axle  respec- 
tively being  represented 
by  R  and  r.  But 

r  :  R  :  :  d  :  D,  and  r  :  R  :  :  c  :  C. 

In  other  words,  the  mechanical  advantage  of  this  machine 
equals  the  ratio  between  the  radii,  diameters,  or  circumfer- 
ences of  the  wheel  and  of  the  axle. 


FIG.  84. 


140 


SCHOOL  PHYSICS. 


FIG.  85. 


136.    Modifications  of  the  Wheel  and  Axle.  —  It   is  not 
necessary  that  an  entire  wheel  be  present,  a  single  spoke 

or  radius  being  sufficient 
for  the  application  of  the 
power,  as  in  the  case  of 
the  windlass  (Fig.  84) 
or  the  capstan  (Fig.  85). 

(a)  In  the  differential  or 
Chinese  windlass,  different 
parts  of  the  cylinder  have 
different  diameters,  the  rope 
winding  upon  the  larger  and 
unwinding  from  the  smaller 
parts.  By  one  revolution,  the  load  is  lifted  a  distance  equal  to  the 
difference  between  the  circumferences  of  the  two  parts  of  the  axle. 

(6)  The  advantage  of  the  wheel  and  axle  may  be  increased  by 
combining  several,  so  that  the  axle  of  the  first  may  act  on  the  wheel 
of  the  second,  and  so  on.     The  arrange- 
ment is  closely  analogous  to  the  compound 
lever.     The  transmission  of  motion  may 
be  effected  in  three  or  more  ways  :  — 

(1)  By  the   friction   of  their   circum- 
ferences, as  in  some  sewing  machines. 

(2)  By  bands  or  belts,  as  in  a  turning 
lathe,  bicycle,  or  sewing  machine. 

(3)  By  teeth  or  cogs,  as  in  Fig.  86.     In 
any  case,  the  advantage  may  be  computed 
by  applying  the  general  laws  of  machines 
(§  124). 

CLASSROOM  EXERCISES. 

1.  The  pilot  wheel  of  a  boat  is  3  feet  in  diameter;  the  axle,  6 
inches.     The  resistance  of  the  rudder  is  180  pounds.     What  power 
applied  to  the  wheel  will  move  the  rudder  ? 

2.  Four  men  are  hoisting  an  anchor  of  1  ton  weight.     The  barrel 
of  the  capstan  is  8  inches  in  diameter.     The  circle  described  by  the 
handspikes  is  6  feet  8  inches  in  diameter.      How   great  a  pressure 
must  each  of  the  men  exert  ? 


FIG.  80. 


SIMPLE    MACHINES. 


141 


3.  With  a  capstan,  four  men  are  raising  a  1,000-pound  anchor. 
The  barrel  of  the  capstan  is  a  foot  in  diameter.    The  handspikes  used 
are  5  feet  long.    Friction  equals  10  per  cent  of  the  weight.    How  much 
force  must  each  man  exert  to  raise  the  anchor  ? 

4.  The  circumference  of  a  wheel  is  8  feet;   that  of  its  axle,  16 
inches.     The  weight,  including  friction,  is  85  pounds.      How  great 
a  power  will  be'required  to  raise  it  ? 

5.  A  power  of  70  pounds,  on  a  wheel  whose  diameter  is  10  feet, 
balances  300  pounds  on  the  axle.     Give  the  diameter  of  the  axle. 

6.  An  axle  10  inches  in  diameter,  fitted  with  a  winch  18  inches 
long,  is  used  to  draw  water  from  a  well,     (a)  How  great  a  power 
will  it  require  to  raise  a  cubic  foot  of  water  which  weighs  62£  pounds  ? 
(6)  How  much  to  raise  20  liters  of  water  ? 

7.  A  capstan  whose  barrel  has  a  diameter  of  14  inches  is  worked 
by  two  handspikes,  each  7  feet  long.     At  the  end  of  each  handspike 
a  man  pushes  with  a  force  of  30  pounds ;  2  feet  from  the  end  of  each 
handspike  a  man  pushes  with  a  force  of  40  pounds.     Required  the 
effect  produced  by  the  four  men. 

8.  How  long  will  it  take  a  horse,  working  at  the  end  of  a  bar  7 
feet  long,  the  other  end  being  in  a  capstan  which  has  a  barrel  of  14 
inches'  diameter,  to  pull  a  house  through  5  miles  of  streets,  if  the 
horse  walks  at  the  rate  of  2|  miles  an  hour? 

9.  Give  a  good  definition  and  illustration  of  "inductive  reasoning." 
(Get  your  information  from  any  available  source,  but  get  it.) 


137.    A 


i_ 


FIG. 


Pulley  is  a  wheel  having  a  grooved  rim  for  carry- 
ing a  rope  or  other 
^yj\  line,  and  turning  on 

an  axis  carried  in  a 
;  frame,  called  a  pulley 

block.     The  pulley  is 

fixed  if  the  block    is 

stationary  (Fig.  87)  ; 

the  pulley  is  movable 

if    the    block    moves 

during   the  action  of 

the  power  (Fig.  88). 


FIG.  88. 


142 


SCHOOL  PHYSICS. 


(a)  The  pulley  is  a  lever  with  equal  arms  of  the  first  or  second  class, 
but,  when  it  moves,  the  attachments  of  the  forces  are  moved.  The 
underlying  fact  that  enables 
the  pulley  to  afford  any  me- 
chanical advantage  is  the 
uniformity  of  the  tension  of 
the  cord  in  all  of  its  parts, 
the  pulley  itself  serving  only 
to  diminish  the  friction. 


FIG.  89. 


138.  Systems  of  Pul- 
leys. —  Combinations 
of  pulleys  are  made  in 
great  variety.  In  the 
forms  most  commonly 
used,  one  continuous  cord  passes 
around  all  the  pulleys.  Fre- 
quently two  or  more  sheaves  are 
mounted  in  the  same  block  and 
turn  on  the  same  axis,  as  in  the 
common  block  and  tackle,  shown  in  Fig.  90. 


FIG.  90. 


FIG.  91. 


(a)  Another  arrangement,  sometimes 
seen  on  board  merchant  ships,  requires  a 
separate  cord  for  each  pulley.  (See  Fig.  102.) 

(&)  In  the  differential  pulley,  an  endless 
chain  is  reeved  upon  a  solid  wheel  that  has 
two  grooved  rims  and  is  carried  in  a  fixed 
block  above,  and  upon  a  pulley  below,  as  is 
shown  in  Fig.  91.  The  two  rims  of  the 
single  wheel  in  the  upper  block  have  dif- 
ferent diameters,  and  carry  projections  to 
keep  the  chain  from  slipping  on  them. 
When  the  chain  is  pulled  down  until  the 
upper  wheel  turns  once  upon  its  axis,  the 
chain  between  the  two  pulleys  is  shortened 
by  the  difference  between  the  circumferences 


SIMPLE    MACHINES.  143 

of  the  two  rims  of  the  upper  wheel,  and  the  load  is  lifted  half  that 
distance.  This  device  avoids  the  use  of  inconveniently  long  ropes  or 
chains.  In  Fig.  91,  the  hoisting  apparatus  is  hooked  into  the  triangu- 
lar frame  of  a  traveler  which  is  supported  by  rollers  on  the  rail- 
way overhead. 

139.  Mechanical  Advantage  of  the  Pulley.  —  With  the 
ordinary   arrangement    of    pulleys,   like    the    block    and 
tackle,  the  part  of  the  cord  to  which  the  power  is  applied 
carries  but  a  part  of  the  load,  the  magnitude  of  that  part 
varying  inversely  as  the  number  of  sections  into  which 
the  movable  pulley  divides  the  load.      With  pulleys  thus 
arranged,  a  given  power  will  support  a  weight  as   many 
times  as  great  as  itself  as  there  are  parts  of  the  cord  sup- 
porting the  movable  block. 

W=Pxn. 

(a)  In  the  case  of  the  differential  pulley,  the  mechanical  advan- 
tage may  be  determined  by  the  laws  given  in  §  124. 

(6)  In  all  experiments  to  determine  the  mechanical  advantage 
of  a  system  of  pulleys,  as  in  all  similar  experiments,  see  that  the 
apparatus  is  in  equilibrium  before  applying  P  and  W. 

140.  An  Inclined  Plane  is  a  smooth,  hard,  inflexible  surface, 
inclined    so    as    to    make    an 

oblique  angle  with  the  horizon. 

(a)  When  a  body  is  placed  on 
an  inclined  plane,  the  gravity  pull 
is  resolved  into  two  component 
forces.  One  of  these  acts  perpen- 
dicularly to  the  plane,  producing 
pressure  on  it,  the  other  compo-  FIG.  92. 

nent  tending  to  produce    motion 

down  the  plane.  To  resist  this  last-mentioned  tendency,  and  thus 
to  hold  the  body  in  its  position,"  a  force  may  be  applied  in  three 
ways :  — 


144 


SCHOOL  PHYSICS. 


(1)  In  a  direction  parallel  to  the  length  of  the  plane. 

(2)  In  a  direction  parallel  to  the  base  of  the  plane;   i.e.,  hori- 
zontal. 

(3)  In  a  direction  parallel  to  neither  the  length  nor  the  base. 

141.    Mechanical  Advantage  of  the  Inclined  Plane.  —  The 
mechanical  advantage  to  be  derived  from  the  use  of  an 
inclined  plane  varies  with  the  three 
conditions  above  given. 

20  Kg. 


10  "Kg. 


FIG.  93. 


(1)  When  a  given  power  acts  par- 
allel to  an  inclined  plane,  it  will  sup- 
port a  weight  as  many  times  as  great 
as  itself  as  the  length  of  the  plane  is 
times  as  great  as  its  vertical  height. 

(2)  When  a  given  power  acts  horizontally,  it  will  sup- 
port  a   weight  as   many   times    as  great   as  itself  as    the 
horizontal  base  of  the  plane  is  times  as  great  as  its  vertical 
height. 

(3)  When   the   power   acts   in  a  direction   parallel  to 
neither  the  length  nor  the  base,  no  law  can  be  given. 
The  ratio  of  the  power  to  the  weight  may  be  determined 
trigonometrically,  or,  with 

approximate  accuracy,  by 
resolving  the  force  of  grav- 
ity, the  construction  and 
measurement  being  care- 
fully done. 

(a)  In  Fig.  9£,  LM  repre- 
sents an  inclined  plane  on  which 
a  ball  is  to  be  supported  by  a 
force  acting  parallel  to  the 
plane.  Represent  the  gravity  of  W  by  the  vertical  line,  WC,  and 


SIMPLE   MACHINES.  145 

resolve  it  into  two  components.  WD  produces  pressure  on  the  plane, 
and  WB  draws  the  body  down  the  plane.  A  force  represented  by 
WB',  the  equilibrant  of  WB,  will  just  balance  the  downward  pull  of 
WB,  and  hold  the  ball  in  position.  From  the  similarity  of  the  tri- 
angles, CWB  and  LMN,  it  may  be  proved  that 

WB  :  WC  :  :  MN  :  ML. 

Careful  construction  and  measurement  will  give  the  same  result. 
But  WB,  or  its  equal,  WB'}  represents  the  power,  and  WC  represents 
the  weight  of  the  body.  MN  represents  the  height  of  the  plane,  and 
ML  its  length.  Therefore 

P  :  W  :  :  h  :  I. 

By  similarly  resolving  the  force  of  gravity  into  two  components, 
one  perpendicular  to  the  plane  and  the  other  horizontal,  the  second 
law  as  given  above  may  be  established. 


CLASSROOM  EXERCISES. 

1 .  With  a  fixed  pulley,  what  power  will  support  a  weight  of  50 
pounds? 

2.  With  a  movable  pulley,  what  power  will  support  a  weight  of 
50  pounds? 

3.  With  block  and  tackle,  the  fixed  block  having  four  sheaves  and 
the  movable  block  having  three,  what  weight  may  be  supported  by  a 
power  of  75  pounds  ?    If  an  allowance  of  |  is  made  for  friction  and 
rigidity  of  ropes,  what  is  the  maximum  weight  that  may  be  thus 
supported  ? 

4.  With  a  system  of  five  movable  pulleys,  one  end  of  the  rope  being 
attached  to  the  fixed  block,  what  power  wTill  raise  a  ton  ? 

5.  If,  in  the  system  mentioned  in  Exercise  4,  the  rope  is  attached 
to  the  movable  block,  what  power  will  raise  a  ton?    If  an  allowance 
of  25  per  cent  is  made  for  friction  and  rigidity  of  ropes,  what  power 
will  be  required  ? 

6.  With   a   pulley   of   six   sheaves   in  each   block,  what  is  the 
least   power  that  will    support  a  weight  of   1,800  pounds,   allow- 
ing £  for  friction?     What  will    be   the    relative   velocities    of  P 
and   W? 

10 


146  SCHOOL   PHYSICS. 

7.  Figure  a  set  of  pulleys  by  which  a  power  of  50  pounds  will 
support  a  weight  of  250  pounds. 

8.  A  boy  who  can  lift  only  100  pounds  wishes  to  put  a  barrel  of 
flour  (196  pounds)  into  a  wagon-box  5  feet  above  the  ground.     He 
backs  the  wagon  to  one  end  of  a  plank  20  feet  long  and  weighing 
125  pounds.     Show  that  he  can,  without  help,  use  the  plank  as  an 
inclined  plane  for  his  purpose,  and  state  how  much  force  he  exerts 
(a)  in  getting  the  plank  into  position,  and  (6)  how  much  in  lifting 
the  flour?     (c)  How  much  work  does  he  perform  in  lifting  the  flour  ? 

Am.  (a)  62|  pounds;  (b)  49  +  pounds. 

9.  How    much    energy   must  be   expended  to  pull   a   100-pound 
•weight  up  an  inclined  plane  10  feet,  the  vertical  ascent  accomplished 
being  6  feet,  and  the  coefficient  of  friction  being  0.2? 

10.  The  base  of  an  inclined  plane  is  10  feet ;  the  height  is  3  feet. 
What  force,  acting  parallel  to  the  base,  will  balance  a  weight  of 
2  tons? 

11.  An  incline  has  its  base  10  feet ;  its  height,  4  feet.     How  heavy 
a  ball  will  50  pounds  power  roll  up  ? 

12.  How  great  a  power  will  be  required  to  support  a  ball  weigh- 
ing 40  pounds   on   an   inclined  plane  whose  length  is  8  times  its 
height? 

13.  A  weight  of  800  pounds  rests  upon  an  inclined  plane  8  feet 
high,  being  held  in  equilibrium  by  a  force  of  25  pounds  acting  parallel 
to  the  base.     Find  the  length  of  the  plane. 

14.  A  load  of  2  tons  is  to  be  lifted  along  an  incline.     The  power  is 
75  pounds.     Give  the  ratio  of  the  incline  that  may  be  used. 

15.  A  1,500-pound  safe  is  to  be  raised  5  feet.     The  greatest  power 
that  can  be  applied  is  250  pound's.    Give  the  dimensions  of  the  shortest 
inclined  plane  that  can  be  used  for  that  purpose. 

16.  A  weight  of  400  pounds  is  being  raised  by  a  block  and  tackle. 
One  end  of  the  rope  is  fastened  to  the  upper  block.     Each  block  has 
two  sheaves  and  weighs  10  pounds.     What  is  the  pressure  on  the 
support  of  the  upper  block  ?    Disregard  the  weight  of  the  rope. 

Ans.  522    pounds. 

142.  A  Wedge  is  a  triangular  prism  of  hard  material, 
fitted  to  be  driven  between  objects  that  are  to  be  sepa- 
rated, or  into  anything  that  is  to  be  split.  It  is  simply  a 
movable  inclined  plane,  or  two  such  planes  united  at  their 


SIMPLE   MACHINES. 


147 


bases.  The  power  is  generally  applied  in  repeated  blows 
on  the  thick  end  or  "head."  For  a  wedge  thus  used,  no 
definite  law  of  any  prac- 
tical value  can  be  given, 
further  than  that,  with  a 
given  thickness,  the  longer 
the  wedge,  the  greater  the 
mechanical  advantage. 


FIG.  95. 


143.  A  Screw  is  a  cylinder,  generally  of  wood 
or  metal,  with  a  spiral  ridge  (the  thread)  wind- 
ing about  its  circumference. 
The  thread  works  in  a  nut, 
within  which  there  is  a  cor- 
responding spiral  groove  to 
receive  the  thread.  That  the 
screw  is  a  modified  inclined 
plane,  may  be  shown  by 
winding  a  triangular  piece 
of  paper  around  a  cylinder, 
FIG.  97.  as  shown  in  Fig.  98. 

(a)  The  power  is  generally  applied  by  a 

wheel  or  a  lever,  and  moves 

through    the    circumference 

of  a  circle.      The   distance 

between     two     consecutive 

turns  of  any  one  continuous 

thread,  measured  in  the  di- 
rection  of  the   axis  of  the 

screw,  is  called  the  pitch  of 

the  screw. 

(6)  The  screw  is  largely  used  where  great  FIG.  99. 

resistances  are  to  be  overcome,  as  in  raising  buildings,  compressing 
hay  or  cotton,  propelling  ships,  etc.     It  is  also  used  in  accurate 


FIG.  98. 


148  SCHOOL  PHYSICS. 

measurements  of  small  distances,  of  which  application  the   sphe- 
rometer,  and  the  micrometer  calipers,  afford  good  illustrations. 

144.  Mechanical  Advantage   of  the  Screw.  —  With  the 
screw,  a  given  power  will  support  a  weight  as  many  times  as 
great  as  itself  as  the  circumference  described  by  the  power  is 
times  as  great  as  the  pitch  of  the  screw. 

145.  Compound  Machines.  —  We  have  now  considered 
each  of  the  six  traditional  simple  machines.     When  any 
two  or  more  of   these  machines  are  combined,  the  me- 
chanical   advantage    may   be    found    by   computing    the 
effect  of  each  separately,  and  then  compounding  them ; 
or   by   finding    the    weight    that    the   given   power   will 
support,  using  the  first  machine  alone,   considering  the 
result  as  a  new  power  acting  upon  the  second  machine, 
and  so  on. 

CLASSROOM  EXERCISES. 

1.  A  bookbinder  has  a  press,  the  screw  of  which  has  a  pitch  of  i  of 
an  inch.     The  nut  is  worked  by  a  lever  that  describes  a  circumference 
of  8  feet.     How  great  a  pressure  will  a  power  of  15  pounds  applied  at 
the  end  of  the  lever  produce,  the  loss  by  friction  being  equivalent  to 
240  pounds  ? 

2.  A  screw  has  11  threads  for  every  inch  in  length.     If  the  lever 
is  8  inches  long,  the  power  50  pounds,  and  friction  absorbs  ^  of  the 
energy  used,  what  resistance  may  be  overcome  by  it? 

3.  A  screw  with  threads  lj  inches  apart  is  driven  by  a  lever  4|  feet 
long.     What  is  the  mechanical  advantage  of  the  apparatus? 

4.  How  great  a  pressure  will  be  exerted  by  a  power  of  15  pounds 
applied  to  a  screw  whose  head  is  1  inch  in  circumference,  and  whose 
threads  are  $•  of  an  inch  apart  ? 

5.  At  the  top  of   an  inclined  plane  that  rises  1  foot  in  20  is  a 
wheel  and  axle.     The  radius  of  the  wheel  is  2|  feet;  radius  of  axle, 
4|  inches.     What  load  may  be  lifted  by  a  boy  who  turns  the  wheel 
with  a  force  of  25  pounds  ? 


SIMPLE   MACHINES. 


149 


6.  In  moving  a  building,  the  horse  is  harnessed  to  the  end  of 
a  lever  7  feet  long,  acting  on  a  capstan  barrel  11  inches  in  diameter. 
On  the  barrel  winds  a  rope  belonging  to  a  system  of  2  fixed  and 
3  movable  pulleys.     What  force  will  be  exerted  by  500  pounds  power, 
allowing  £•  for  loss  by  friction  ? 

7.  In  raising  a  building,  why  do  the  men  who  work  the  jackscrews 
pull  upon  the  levers  by  a  series  of  jerks  instead  of  steady  pulls? 


W 


LABORATORY  EXERCISES. 

Additional  Apparatus.  —  Pulleys  and  cords  that  are  strong  enough 
to  support  at  least  100  pounds.* 

1.  Experimentally  determine  the  ratio  of  power  to  weight  with 
pulleys   arranged  as  shown 
in  Fig.  100. 

2.  Determine  the  loss  due 
to  friction  and  to  the  rigidity 
of  the  ropes  used  in  Exer- 
cise 1. 

3.  Experimentally     deter-  pIG  JQQ 
mine  the  ratio  of  power  to 

weight  with  pulleys  arranged  as  shown  in  Fig.  101. 

4.  Show  how  the  work  done  at  P,  in  Exercise  3,  compares  with 

the  work  done  at  W,  and  account 

for  any  difference  if  you  find 
any  to  exist. 

5.  Experimentally  Determine 
the  ratio  between  P  and  W  with 
pulleys  arranged  as  shown  in 
Fig.  102.     Determine  the  static 
law  of  such  a  combination. 

6.  The  height  of  an  inclined 

plane  is  £  its  horizontal  base. 

A  globe  weighing  250  Kg.  is  sup- 
ported in  place  by  a  force  acting 

at  an  angle  of  45°  with  the  base. 

The  pressure  of  the  globe  upon 

the  plane  is  less  than  250  Kg. 

By  construction  and  measure- 
ment, determine  the  magnitude  of  the  support- 
ing force. 


Fm.  102. 


150  SCHOOL  PHYSICS. 

7.  With  the  conditions  as  given  in  Exercise  6,  except  that  the 
pressure  of  the  globe  upon  the  plane  is  more  than  250  Kg.,  determine 
the  magnitude  of  the  supporting  force. 

8.  Place  the  board  used  in  Experiment  7  so  that  it  may  be  used 
again  as  an  inclined  plane.     Tie  one  end  of  a  cord  to  the  carriage 
used  in  the  same  experiment,  and  the  other  end  to  a  spring-balance. 
The  dynamometer  and  the  cord  are  to  be  used  in  pulling  the  carriage 
up  the  incline.     Varying  the  load  and  the  inclination  of  the  plane  in 
each  case,  verify  the  statements  made  in  §  141.     Be  sure  that  the 
board  does  not  bend  or  sag  under  the  load.     Watch  for  error  in  the 
zero  point  of  the  balance  when  held  in^  different  positions,  and,  if  any 
is  detected,  make  correction  for  it.     To  determine  the  correction  to 
be  made  for  friction,  find  first  the  pull  necessary  to  move  the  carriage 
up  the  incline  at  a  uniform  speed,  and  then  the  pull  which  will  allow 
it  to  move  down  the  incline  at  a  uniform  speed.     The  difference  be- 
tween these  two  pulls  will  be  twice  the  force  required  to  overcome  the 
friction,  and  the  average  of  the  two  pulls  will  be  the  force  that  would 
be  required  if  friction  could  be  eliminated. 

9.  Arrange  an  inclined  plane  so  that  its  base  shall  be  1|  times  its 
height.     Draw  a  diagram  for  the  resolution  of  the  force  of  gravity 
and  determine  the  tendency  of  a  ball  that  weighs  7^  pounds  to  roll 
down  the  plane,  and  the  pressure  of  the  ball  on  the  plane.     Suspend 
the  ball  by  two  spring-balances,  so  that  one  of  them  is  drawn  par- 
allel to  the  plane  and  the  other  perpendicular  to  it  when  the  ball  is 
just  lifted  off  the  plane.     Note  the  reading  of  the  dynamometers  and 
compare  them  with  the  computed  results. 


VII.    THE  MECHANICS   OE  LIQUIDS. 

146.  Compressibility  and  Elasticity  of  Liquids.  —  Liquids 
are  nearly  incompressible.  When  the  pressure  is  removed, 
the  liquids  regain  their  former  volume,  showing  thus 
their  perfect  elasticity.  The  practical  incompressibility 
of  liquids  is  of  great  mechanical  importance. 


THE  MECHANICS  OF  LIQUIDS.  151 


Liquid  Pressure. 

Experiment  58.  —  Fill  a  small  bottle  with  water,  hold  a  Prince 
Rupert  drop  in  its  mouth,  and  break  off  the  tapering  end  of  the 
"  drop."  The  whole  "  drop  "  will-  be  instantly  shattered,  and  the  force 
of  the  concussion  transmitted  in  every  direction  to  the  bottle,  which 
will  be  thus  broken.  These  "  drops  "  are  not  expensive. 

Experiment  59.  —  Tie  a  piece  of  thin  sheet  rubber  (such  as  you  can 
get  from  the  druggist  or  dentist,  or  from  a  broken  toy  balloon)  over 
the  large  end  of  a  lamp-chimney.  Reinforce  the  other  end  by  wind- 
ing upon  it  a  dozen  turns  of  wrapping  twine,  and  fit  it  with  a  fine- 
grained cork  or  rubber  stopper  through  which  passes  snugly  a  bit  of 
glass  tubing.  (See  Chemis- 
try, Appendices  4  [6]  and  9.) 
Connect  the  glass  tubing  and 
a  supported  funnel  by  two 
or  three  feet  of  rubber  tub- 
ing. Fill  the  apparatus  with 
water,  loosening  the  cork  for  FIGi  N)3. 

a  moment  to  allow  the  escape 

of  air.  See  that  the  funnel  is  still  half  full  of  water  and  elevated 
above  the  chimney.  Notice  the  effect  of  the  water  pressure  on  the 
sheet  rubber.  Hold  the  chimney  in  various  positions,  keeping  the 
center  of  the  sheet  rubber  at  a  uniform  distance  below  the  level  of 
the  funnel,  and  notice  whether  the  elastic  sheet  is  stretched  more  or 
less  when  the  liquid  pressure  upon  it  is  horizontal,  upward,  or  down- 
ward. Then  try  it  at  varying  distances  below  the  level  of  the  water 
in  the  funnel,  and  determine  whether  such  vertical  distance  or  "head" 
has  any  relation  to  the  pressure. 

Experiment  60.  —  To  the  cork  of  Experiment  59,  fit  a  bit  of  glass 
tubing  that  has  been  drawn  to  a  jet  at  the  outer  end.  Hold  the 
chimney  in  different  positions  and  at  different  depths,  adding  water 
as  may  be  necessary  to  keep  a  constant  level  in  the  funnel. 

147.  Transmission  of  Pressure. — Fluids  transmit  pres- 
sures in  every  direction. 

(a)  Fig.  104  represents  a  number  of  balls  placed  in  a  vessel. 
Imagine  these  balls  to  have  perfect  freedom  of  motion  and  perfect 


152 


SCHOOL  PHYSICS. 


FIG.  104. 


elasticity.  It  is  evident  that  if  a  downward  pressure,  say  of  10  grams, 
is  applied  to  2,  it  will  force  5  and  4  toward  the  left,  and  6,  7,  and 
8  toward  the  right,  thus  forming  lateral  pressure.  This  motion  of 
5  will  force  1  upward,  and  9  downward,  etc. 
Owing  to  the  perfect  elasticity  and  freedom  of 
motion,  there  will  be  no  loss,  and  the  several 
balls  will  be  moved  just  as  if  the  original  pres- 
sure had  been  applied  directly  to  each  one.  The 
pressure  will  be  thus  transmitted  to  all  of  the 
balls  without  loss,  and  the  total  pressure  exerted 
on  the  sides  of  the  vessel  will  equal  10  grams 
multiplied  by  the  number  of  balls  that  touch  the  sides.  It  makes  no 
difference  with  the  result  whether  the  pressure  exerted  by  2  was  the 
result  of  its  own  weight  only,  this  weight  together  with  the  weight 
of  overlying  balls,  or  both  of  these  with  still  additional  pressure. 

(6)  Disregarding  viscosity,  we  may  consider  a  fluid  to  be  made 
up  of  molecules  having  the  perfect  elasticity  and  freedom  of  motion 
assumed  for  the  balls  just  discussed.  Hence,  when  pressure  is  applied 
to  one  or  more  of  the  molecules  of  a  fluid,  the  pressure  will  be  trans- 
mitted as  now  explained. 

148.  Pascal's  Law.  — Pressure  exerted  anyivhere  upon  a 
liquid  inclosed  in  a  vessel  is  transmitted  undiminished  in  all 
directions,  and  acts  with  the 
same  force  upon  all  equal  sur- 
faces, and  in  a  direction  at 
right  angles  to  those  surfaces. 

(a)  Provide  two  communicating 
tubes  of  unequal  sectional  area. 
When  water  is  poured  into  these, 
it  will  stand  at  the  same  height  in 
both  tubes,  —  a  fact  which  of  itself 
partly  confirms  the  law  above  given. 
If,  by  means  of  a  piston,  the  water 
in  the  smaller  tube  is  subjected  to 
pressure,  the  pressure  will  force  the 
water  back  into  the  larger  tube, 
and  raise  its  level  there.  To  prevent  this  result,  a  piston  must  be 


FIG.  105. 


THE   MECHANICS   OF  LIQUIDS. 


158 


fitted  to  the  larger  tube,  and  held  there  with  a  greater  force.    If,  for 
example,  the  smaller  piston  has  an  area  of  1  sq.  cm.,  and  the  larger 
piston  an  area  of  16  sq.  cm.,  a  weight 
of  1  Kg.  may  be  made  to  support  a 
weight  of  16  Kg. 

149.    The  Hydraulic  Press.  - 

Pascal's  law  finds  an  important 
application  in  the  hydraulic 
press,  in  the  more  common 
forms  of  which  the  pressure  of 
a  piston  operated  by  a  lever  is 
transmitted  through  a  pipe  to 
a  piston  of  larger  area.  The 
press  is  represented  in  section  by  Fig.  107,  and  in  per- 
spective by  Fig.  108. 

(a)  If  the  power  arm  of  the  lever  is  ten  times  as  long  as  the  weight 
arm,  a  power  of  50  Kg.  will  exert  a  pressure  of  500  Kg.  upon  the 


FIG.  10G. 


FIG.  107. 

water  beneath  the  piston,  a.     If  this  piston  has  a  sectional  area  of 
1  sq.  cm.,  and  the  piston  in  B  has  an  area  of  500  sq.  cm.,  then  the  pres- 


154 


SCHOOL  PHYSICS. 


sure  of  500  Kg.  exerted  by  the  small  piston  will  produce  a  pressure 
of  500  Kg.  x  500  or  250,000  Kg.  upon  the  lower  surface  of  the  large 
piston. 


FIG.  108. 


Pressure  due  to  Gravity. 

Experiment  61.  —  Make  a  small  hole  in  the  bottom  of  a  tin  fruit- 
can  or  similar  vessel.  Push  the  can  downward  into  water  until  the 
open  mouth  of  the  can  is  "  near  the  water's  edge."  The  liquid  will 
spurt  upward  through  the  hole  in  a  little  jet.  Why? 

Experiment  62.  —  Get  a  lamp-chimney,  preferably  cylindrical. 
With  a  diamond  or  a  steel  glass-cutter,  cut  a  disk  of  window  glass 
a  little  larger  than  the  cross-section  of  the  lamp-chimney.  Pour  some 
fine  emery  powder  on  the  disk,  and  rub  one  end  of  the  chimney  upon 
it,  thus  grinding  them  until  they  fit  accurately.  With  wax,  fasten  a 


THE   MECHANICS  OF  LIQUIDS. 


155 


thread  to  the  center  of  the  ground  surface  of  the  disk,  and  draw  that 
surface  against  the  ground  end  of  the  chimney.  Holding  the  chimney 
in  the  hand,  or  supporting  it  in  any 
convenient  way,  place  it  in  water  as 
shown  in  Fig.  109.  The  upward  pres- 
sure of  the  water  will  hold  the  disk  in 
place.  Pour  water  carefully  into  the 
tube;  the  disk  will  fall  as  soon  as  the 
weight  of  the  water  in  the  chimney, 
plus  the  weight  of  the  disk,  exceeds  the 
upward  pressure  of  the  water. 


FlG 


Experiment  63.  —  Into  a  U-tube,  pour 

enough  mercury  to  fill  each  arm  to  the 

depth  of  3  or  4  cm.     Place  the  U-tube 

upon  a  table,  and  hold  it  upright  by 

any  convenient  means.    Back  of  it,  and 

resting  against  it,  stand  a  card  having 

a  horizontal  line,  a,   drawn   on   it  to 

mark  the  level  of  the  mercury  in  the 

two  arms  of  the  tube.     To  one  arm,  attach  the  neck  of  a  funnel  by 

means  of  a  bit  of  rubber  tubing.  The  funnel  may  be  held  by  the 

ring  of  a  retort  stand.  Pour  water 
slowly  into  the  funnel  until  it  is 
nearly  full,  and  mark  the  level  of 
the  water  by  a  suspended  weight 
or  other  means.  In  one  arm,  the 
mercury  will  be  depressed  below 
the  line  marked  on  the  card;  in 
the  other  arm,  it  will  be  raised 
above  it  an  equal  distance.  Mark 
these  two  mercury  levels  by  dotted 
horizontal  lines  on  the  card.  Re- 
move the  funnel  and  replace  it  by 
a  funnel-  or  thistle-tube,  making 
the  connection  by  means  of  a  per- 
forated cork.  Pour  water  into  the 
funnel-tube  until  it  stands  at  the 
level  indicated  by  the  suspended 
FIG.  110.  weight,  being  careful  that  no  air  is 


156 


SCHOOL   PHYSICS. 


confined  in  the  tubes.  Although  much  less  water  is  in  the  funnel-tube 
than  was  in  the  funnel,  it  forces  the  mercury  into  the  position  indi- 
cated by  the  dotted  lines  on  the  card.  The  downward  pressure  of  the 
water  in  each  case  is  measured  by  a  mercury  column  with  a  height,  ce, 
equal  to  the  vertical  distance  between  the  two  dotted  lines. 

Experiment  64.  —  Provide  several  glass  vessels,  open  at  each  end, 
and  having  equal  bases,  but  varying  shapes  and  capacities.  In  any 
convenient  way,  support  one  of  them,  as  M  in  Fig.  111.  Close  the 
lower  end  of  the  vessel  with  a  glass  or  metal  disk,  ground  to  fit  it 


FIG.  111. 


water-tight,  the  disk  being  supported  by  a  thread  carried  from  one 
end  of  a  balance-beam.  Place  known  weights  in  the  scale-pan  at  the 
other  end  of  the  beam,  so  that  the  disk  shall  be  held  firmly  in  place. 
Pour  water  carefully  into  the  upper  or  open  end  of  the  vessel,  until 
the  pressure  loosens  the  disk  and  allows  a  little  to  escape.  By  an 
index  rod,  suspended  weight,  or  other  convenient  means,  mark  the 
upper  level  of  the  water  at  the  moment  when  some  of  the  liquid 
begins  to  escape  below.  Repeat  the  experiment  with  the  other  ves- 
sels in  succession,  using  the  same  counterpoise  in  each  case.  The 
disk  will  be  loosened  when  the  water  has  reached  the  marked  level, 


THE   MECHANICS   OF   LIQUIDS.  157 

although  the  quantity  of  water  used  varies.  The  glass  vessels  for 
this  experiment  may  be  easily  secured  by  using  glass  tubing,  a  glass 
funnel,  corks,  lamp  chimneys,  etc.  (See  Avery's  Chemistry,  Appen- 
dix 4.) 

150.  Liquid  Pressure  due  to  Gravity.  —  The  downward 
pressure    of  a  liquid  is  independent  of   the  shape   of  the 
containing  vessel  and  of  the  quantity  of  the  liquid.     It  is 
proportional  to  the  depth  of  the  liquid  and  the  area  of  the 
base. 

151.  Rules  for  Liquid  Pressure. 

(1)  To  find  the  downward  or  the  upward  pressure  on  any 
submerged  horizontal  surface,  find  the  weight  of  an  imaginary 
column  of  the  given  liquid,  the  base  of  which  is  the  same 
as  the  given  surface,  and  the  altitude  of  which  is  the  same 
as  the  depth  of  the  given  surface  beloiv  the  surface  of  the 
liquid. 

(2)  To  find  the  pressure  upon  any  vertical  surface,  find 
the  weight  of  an  imaginary  column  of  the  liquid,  the  base  of 
which  is  the  same  as  the  given  surface,  and  the  altitude  of 
which,  is  the  same  as  the  depth  of  the  'center  of  the  given 
surface  below  the  surface  of  the  liquid. 

(a)  A  cubic  foot  of  water  weighs  62.42  Ibs.  or  about  1,000  oz. 

Liquid  Level. 

Experiment  65.  —  Remove  the  jet  from  the  cork  used  in  Experi- 
ment 60,  and  insert  in  its  place  a  glass  tube  about  two  feet  long. 
Holding  the  chimney  on  the  table-top  with  this  glass  tube  upright, 
fill  the  apparatus  with  water.  Does  the  water  stand  at  a  higher  level 
in  the  funnel,  or  in  the  tube  V  Raise  and  lower  the  funnel,  and  for 
each  position  notice  the  relation  between  the  liquid  levels  in  the 
funnel  and  the  tube. 


158 


SCHOOL   PHYSICS. 


152.  Communicating  Vessels. — When  any  liquid  is 
placed  in  one  or  more  of  several  vessels  communicat- 
ing with  each  other,  it 
will  not  come  to  rest  un- 
til it  stands  at  the  same 
height  in  all  of  the  ves- 
sels. This  principle  is 
embodied  in  the  familiar 
expression,  "Water seeks 
its  level."  The  princi- 
ple is  illustrated,  on  a 
large  scale,  in  the  sys- 
tem of  pipes  by  which 
water  is  distributed  in 
FIG.  112.  cities. 


CLASSROOM  EXERCISES. 

1.  What  will  be  the  pressure  on  a  dam  in  20  feet  of  water,  the  dam 
being  30  feet  long? 

2.  What  will  be  the  pressure  on  a  dam  in  6  m.  of  water,  the  dam 
being  10  m.  long? 

3.  Find  the  pressure  on  one  side  of  a  cistern  5  feet  square  and  12 
feet  high,  filled  with  water. 

4.  Find  the  pressure  on  one  side  of  a  cistern  2  m.  square  and  4  m. 
high,  filled  with  water. 

5.  A  cylindrical  vessel  having  a  base  of  a  square  yard  is  filled  with 
water  to  the  depth  of  two  yards.     What  pressure  is  exerted  upon  the 
base  ? 

6.  A  cylindrical  vessel  having  a  base  of  a  square  meter  is  filled 
with  water  to  the  depth  of  2  meters.     What  pressure  is  exerted  upon 
the  base  ? 

7.  What  will  be  the  upward  pressure  upon  a  horizontal  plate  a  foot 
square  at  a  depth  of  25  feet  of  water  ? 

8.  What  will  be   the   upward   pressure   upon  a  horizontal   plate 
30  cm.  square  at  a  depth  of  8  m.  of  water? 


THE   MECHANICS   OF   LIQUIDS.  159 

9.  A  square  board  with  a  surface  of  9  square  feet  is  pressed  against 
the  bottom  of  the  vertical  wall  of  a  cistern  in  which  the  water  is  8;^ 
feet  deep.     What  pressure  does  the  water  exert  upon  the  board  ? 

10.  A  cubical  vessel  with  a  capacity  of  1,728  cubic  inches  is  two- 
thirds  full  of  sulphuric  acid,  which  is  1.8  times  as  heavy  as  water. 
Find  the  liquid  pressure  on  one  side  of  the  vessel. 

11.  A  conical  vessel  has  a  base  with  an  area  of  237  sq.  cm.     Its 
altitude  is  38  cm.     It  is  filled  with  water  to  the  height  of  35  cm. 
Find  the  pressure  on  the  bottom.  A  ns.  8,295  g. 

12.  In  Exercise  11,  substitute  inches  for  centimeters,  and  then  find 
the  pressure  on  the  bottom. 

13.  What  is  the  total  liquid  pressure  on  a  prismatic  vessel  con- 
taining a  cubic  yard  of  water,  the  bottom  of  the  vessel  being  2  by 
3  feet? 

14.  The  lever  of  a  hydraulic  press  is  6  feet  long,  the  piston  rod 
being  1  foot  from  the  fulcrum.      The  area  of  the  tube   is  half  a 
square  inch ;  that  of  the  cylinder  is  100  square  inches.      Find  the 
weight  that  may  be  raised  by  a  force  of  75  pounds. 

15.  What  is  the  pressure  on  the  bottom  of  a  pyramidal  vessel  filled 
with  water,  the  base  being  2  by  3  feet,  and  the  height  5  feet  ? 

16.  What  is  the  pressure  on  the  bottom  of  a  conical  vessel  4  feet 
high,  filled  with  water,  the  base  being  20  inches  in  diameter? 

17.  At  what  depth  in  water  will  the  liquid  pressure  be  1  Kg.  per 
square  centimeter? 

18.  A  closed  cylindrical  vessel  30  cm.  high  is  filled  with  water. 
At  the  middle  of  its  height,  a  bent  tube  communicates  with  the  in- 
terior of  the  vessel.     Water  stands  in  this  tube  at  a  height  of  50  cm. 
above  the   middle  of  the  opening  into  the   cylinder.      What  is  the 
liquid  pressure  per  square  centimeter  on  the  upper  end  of  the  cylin- 
der?   On  the  lower  end? 

19.  An  upright  cylindrical  jar  having  a  base  of  100  sq.  cm.  and  a 
height  of  20  cm.  is  filled  with  water.      An  open  tube  1  sq.  cm.  in 
cross-section  passes  through  the  cover,  rises  30  cm.  above  it,  and  is 
filled  with  water,     (a)  What  is  the  weight  of  the  water  in  the  jar 
and  tube?     (6)  What  is  the  liquid  pressure  on  the  square  centimeter 
of  the  base  that  lies  exactly  beneath  the  tube?     (c)  What  square 
centimeter  of  the  base  has   a   greater  pressure  ?     (c?)  A  less  pres- 
sure? 

20.  (a)  In  the  case  of  the  jar  and  tube  described  in  Exercise  19, 
what  is  the  liquid  pressure  upon  that  square  centimeter  of  water  at 


160  SCHOOL   PHYSICS. 

the  level  of  the  under  side  of  the  cover  and  beneath  the  tube?  (6)  Is 
the  liquid  pressure  against  each  square  centimeter  of  the  cover  greater, 
or  less,  than  this  ?  (c)  What  is  the  total  liquid  pressure  against  the 
cover  ? 

21.  In  the  case  of  the  jar  and  tube  considered  in  Exercise  20,  sub- 
tract the  total  liquid  pressure  against  the  cover  from  the  total  liquid 
pressure  against  the  base,  and  compare  the  result  with  the  weight  of 
the  water  in  the  jar  and  tube. 

LABORATORY  EXERCISES. 

A dditional  Apparatus,  etc.  —  Stout  glass  tubing ;  an  acid  bottle ;  a 
wine  bottle;  linseed  oil;  rubber  stoppers;  mercury;  tall  hydrometer 
jar. 

1.  Bend  a  piece  of  glass  tubing  into  the  shape  shown  in  Fig.  113, 
and  support  it  upright  in  any  convenient  way.  If  you  remove  the 
top  and  bottom  from  a  box,  and  cut  a  slot  in  one  of  the  remain- 
ing sides,  you  will  have  a  cheap  and  convenient  support,  Remove 
the  funnel  from  the  apparatus  used  in  Experiment  59,  and  connect 
the  rubber  tubing  to  the  glass  tube  at  B.  Half  fill  the 
5 tube  with  water  colored  with  red  ink,  and  it  becomes 
a  pressure  gauge.  The  two  liquid  levels  will  lie  in 
the  same  horizontal  plane.  Mark  this  level  on  the 
open  arm  of  the  gauge,  and  make  it  the  zero  of  a 
scale  extending  upward.  Remember  that  an  eleva- 
tion of  the  liquid  level  above  the  zero  mark  measures 
half  the  difference  between  the  two  liquid  levels  of 
the  gauge.  Place  the  chimney  in  water  at  such  a 
depth  that  the  liquid  pressure  exerted  upon  the  rub- 
ber diaphragm,  and  transmitted  through  all  the  coil- 
ings  of  the  rubber  tubing,  shall  depress  the  surface  at 
m  and  raise  that  at  n,  until  the  difference  of  their 
FIG.  113.  levels,  on,  is,  say,  1  cm.  Note  the  depth  of  the  dia- 
phragm below  the  level  of  the  water.  Hold  the  chim- 
ney in  as  many  different  positions  as  is  convenient,  but  with  the  center 
of  the  diaphragm  at  the  same  depth,  and  note  the  reading  of  the  gauge. 
Sink  the  chimney  to  a  greater  depth  until  on  becomes  successively 
2  cm.,  3  cm.,  etc.,  up  to  the  limit  of  the  gauge.  Compare  your  results 
with  §§  147  and  150,  and  indicate  any  and  all  of  the  statements  therein 
made  that  your  work  confirms. 


THE  MECHANICS  OF  LIQUIDS. 


161 


2.  Cut  the  bottoms  from  a  large  bottle,  and  from  another  bottle  of 
about  equal  height  but  much  less  diameter.     Close  their  mouths  by 
corks  perforated  by  bits  of  glass  tubing.      Support  the  bottomless 
bottles  by  thrusting  their  necks  downward  through  two  holes  bored 
in  the  top  of  a  box.     With  rubber  tubing,  connect  the  glass  tubes 
that  pass  through  the  corks,  making  thus  two  communicating  vessels. 
Half  fill  the  bottles  with  water,  and  mark  the  liquid  level  on  each 
bottle.     Pour  a  measured  quantity  of  oil  into  the  smaller  bottle  until 
it  forms  a  layer  several  centimeters  thick.     The  water-levels  have 
been  changed.     Pour  measured  quantities  of  the  oil  into  the  other 
bottle  until  the  water  is  restored  to  its  marked  levels.     How  do  the 
thicknesses  of  the  two  oil  layers  compare  ?    How  do  the  volumes  of 
the  two  oil  layers  compare?     How  would   the  ratio  between  the 
weights  of  these  oleaginous  additions  differ  from  the  ratio  between 
their  volumes?     With  the  calipers,  measure  the  internal  diameters 
of  the  two  bottles ;  compute  the  cross-section  areas  of  the  two  oil 
cylinders.     How  does  the  ratio  between  these  areas  differ  from  the 
previously  determined  ratios  for  volume  and  weight  ?     How  does  the 
downward  pressure  per  square  centimeter  in  one  branch  correspond 
to  the  pressure  per  square  centimeter  in  the  other  branch  ? 

3.  Provide  a  stout  glass  tube  of  the  shape  shown  in 
Fig.  114.    Pour  mercury  into  the  upper  end  until  it  stands 
at  a  depth  of  1  or  2  cm.  in  the  bend  at  a.     Provide  a 
hydrometer  jar  with  a  depth  as  great  as  the  length,  ce, 
and  nearly  fill  it  with  water.     Lower  the  long  leg  of  the 
tube  into  the  water  about  ^  of  its  length.     Measure  the 
vertical  distance  between  the  levels  of  the  water  within 
and  without  the  tube,  and  call  it  w.     Measure  the  ver- 
tical distance  between  the  two   mercury-levels,   and  call 
it  m.     Lower  the  tube  until  f  of  the  long  arm  is  in  the 
water.     Determine  the  distance  between  the  two  water- 
levels,  and  call  it  w1 ;  determine  the  difference  in  the  two 
mercury-levels,  and  call  it  m'.     Lower  the  tube  until  the 

bend  at  c  rests  on  the  edge  of  the  hydrometer  jar,  and,  as     FIG.  114. 
before,  determine  the  differences  of  the  water-levels  (to") 
and  of  the  mercury-levels  (m").     What  does  the  difference  in  the 
mercury-levels  in  each  case  represent  ?    From  the  data  secured,  test 

the  equality  of  these  ratios  :—  =  —  =  —/    if  you  find  that  the  quan- 
tities are  proportional,  finish  the  following  incomplete  expression 
11 


162  SCHOOL  PHYSICS. 

of  the  relation :  In  the  body  of  a  liquid,  the  upward  pressure  varies 
as  ... 

4.  Considering  m,  m',  and  m"  as  abscissas,  and  w,  w',  and  w"  as 
ordinates,  give  a  graphic  representation  of  the  data  obtained  in  Ex- 
ercise 3.  Is  your  line  straight,  or  curved?  If  it  is  straight,  what  does 
that  fact  show?  If  it  is  curved,  what  does  that  fact  show? 

Principle  of  Archimedes. 

Experiment  66.  —  Suspend  a  stone  or  brick  by  a  slender  cord  or 
fine  wire  from  the  hook  of  a  spring-balance,  and  note  the  reading  of 
the  scale.  Transfer  the  suspended  load  from  air  to  water,  and  note 
the  reading.  Transfer  the  load  to  a  strong  brine,  and  note  the  read- 
ing. Transfer  the  load  to  kerosene,  and  note  again  the  reading.  It 
seems  as  if  the  liquids  help  to  support  the  stone,  with  a  buoyant 
force  of  varying  magnitude. 

Experiment  67. —  From  one  end  of  a  scale-beam,  suspend  a  cylin- 
drical metal  bucket,  b,  with  a  solid  cylinder,  a,  that  fits  accurately 


FIG.  115. 


into  it  hanging  below.     Counterpoise  with  weights  (shot  or  sand)  in 
the  opposite   scale-pan.     Immerse  a  in  water,  and  the  counterpoise 


THE   MECHANICS   OF   LIQUIDS.  163 

will  descend,  as  if  a  had  lost  some  of  its  weight.  Carefully  fill  6  with 
water.  It  will  hold  exactly  the  quantity  displaced  by  a.  Equilibrium 
will  be  restored. 

Experiment  68.  —  For  rough  work,  a  spring-balance  may  take  the 
place  of  the  beam-balance ;  a  tin  pail  may  take  the  place  of  b ;  a 
piece  of  stone  suspended  beneath  the  pail  by  strings  tied  to  the  ears 
of  the  pail  may  take  the  place  of  o;  a  larger  tin  pail  filled  with  water 
and  set  in  a  tin  pan  may  take  the  place  of  the  vessel  of  water  shown 
in  Fig.  115.  Note  the  weight  of  the  smaller  pail,  with  and  without 
the  suspended  stone.  Lower  the  apparatus  so  that  the  stone  shall  be 
immersed  in  the  water,  and  note  the  reading  of  the  scale.  Determine 
the  loss  of  weight  resulting  from  the  immersion  of  the  stone.  The 
volume  of  water  forced  from  the  pail  and  caught  in  the  pan  is  equal 
to  what  other  volume  ?  Remove  the  pan,  immerse  the  stone  as  before, 
pour  the  water  from  the  pan  into  the  upper  pail,  and  note  the  read- 
ing of  the  scale.  To  what  other  reading  is  it  equal?  To  what  is  the 
weight  of  the  water  displaced  by  the  stone  equal  ? 

Experiment  69.  —  Modify  the  experiment  again  as  follows  :  Instead 
of  the  suspended  bucket,  b,  place  a  tumbler  upon  the  scale-pan.  In- 
stead of  the  cylinder,  a,  suspend  any  convenient  solid  heavier  than 
water,  as  a  potato.  Counterpoise  the  tumbler  and  the  potato  with 
weights  in  the  other  scale-pan.  Provide  an  overflow-can  by  inserting 
a  spout  about  6  cm.  long  and  7  or  8  mm.  in  diameter  in  the  side  of  a 
vessel  (as  a  tin  fruit-can)  about  an  inch  below  the  top  of  the  can. 
This  spout  should  slope  slightly  downward.  Fill  the  can  with  water 
and  catch  the  overflow  from  the  spout  in  a  cup.  Throw  away  the  water 
thus  caught.  Wait  a  minute  for  the  spout  to  stop  dripping  and  then 
carefully  immerse  the  potato  in  the  water  of  the  can,  catching  in  the 
cup  every  drop  of  water  that  overflows.  Wait  a  minute  for  the  spout 
to  stop  dripping.  The  equilibrium  of  the  balance  is  destroyed,  but  it 
may  be  restored  by  pouring  into  the  tumbler  the  water  that  was  dis- 
placed by  the  potato  and  caught  in  the  cup. 

-Experiment  70. —  Provide  a  wooden  cube  just  5  cm.  on  an  edge. 
Coat  it  with  shellac  varnish,  or  dip  it  into  hot  paraffins.  -  Weigh  it; 
also  weigh  a  saucer.  Place  a  beaker  or  tumbler  in  the  saucer,  and  fill 
it  with  water.  Stick  two  pins  or  needles  into  one  face  of  the  cube, 
and,  using  them  as  handles,  immerse  the  cube  in  the  water  of  the 
beaker.  Remove  the  beaker,  and  weigh  accurately  the  saucer  and  its 
liquid  contents.  Pour  the  water  from  the  saucer  into  a  graduate,  and 


164 


SCHOOL  PHYSICS. 


measure  it  in  cubic  centimeters.  How  does  its  volume  compare  with 
the  volume  of  the  wooden  cube  ?  What  should  that  quantity  of  water 
weigh  according  to  §  24  (a)  ?  Subtract  the  weight  of  the  saucer  empty 
from  the  weight  of  the  saucer  with  the  liquid  overflow.  How  do 
these  two  weights  of  the  water  compare?  Has  your  work  been  well 
done?  The  weight  of  the  wood  is  what  fractional  part  (expressed 
decimally,  of  course)  of  the  weight  of  the  water  ? 

153.  Archimedes'  Principle.  -(-  It  is  evident  that,  when  a 
solid  is  immersed  in  a  fluid,  it  will  displace  exactly  its  own 
volume  of  the  fluid.J  Immerse  a  solid  cube  one  centi- 
meter on  each  edge  in  water,  s,o  that  its  upper  face  shall 
be  level  and  one  centimeter  below  the  surface  of  the  liquid, 
as  shown  in  Fig.  116.  The  lateral  pressures  upon  any 
two  opposite  vertical  surfaces  of  the  cube,  as  a  and  5, 
are  clearly  equal  and  opposite.  Their  resultant  is  zero. 
They  have  no  tendency  to  move  the  solid.  The  vertical 

pressures  on  the  other  two 
faces,  c  and  d,  are  not  equal. 
The  upper  face  sustains  a  pres- 
sure equal  to  the  weight  of  a 
column  of  water  having  a  base 
one  centimeter  square  (i.e.,  the 
face,  d)  and  an  altitude  equal 
to  the  distance,  dn.  This  imag- 
inary column  of  water  has  a 
volume  of  one  cubic  centimeter 
and  a  weight  of  one  gram.  The 
FIG  11(J  downward  pressure  on  d  is  one 

gram.    As  the  face,  c,  has  the 

same  area  and  is  at  twice  the  depth,  the  upward  pressure 
upon  it  is  two  grams.  The  resultant  of  the  two  vertical 
and  opposite  forces  acting  on  the  cube  is  an  upward  pres- 


THE   MECHANICS   OF  LIQUIDS.  165 

sure  of  one  gram;  i.e.,  the  cube  is  partly  supported  by  a 
buoyant  force  of  one  gram,  which  is  the  weight  of  the  cubic 
centimeter  of  water  that  it  displaces.  No  matter  what 
the  depth  to  which  the  block  is  immersed,  this  net  upward 
pressure,  or  buoyant  effect,  is  always  the  same.  This 
truth,  discovered  by  Archimedes,  may  be  stated  thus  :/A 
body  is  buoyed  up  by  a  force  equal  to  the  weight  of  the  fluid 
that  it  displaces. \  Hence  the  apparent  weight  of  a  body  in 
a  fluid  (e.g.,  water  or  air)  is  less  than  its  true  weight. 
This  buoyant  effect  is  often  spoken  of  as  a  "loss  of 
weight." 

(a)  In  the  above  discussion,  the  effect  of  atmospheric  pressure  is 
left  out  of  the  account.  It  affects  equally  the  top  and  bottom  of  the 
tjlock. 

Flotation. 

Experiment  71.  —  Place  the  tin  can  mentioned  in  Experiment  69, 
upon  one  scale-pan,  and  fill  it  with  water,  some  of  which  will  over- 
flow through  the  spout.  Do  not  let  any  of  the  water  fall  upon  the 
scale-pan.  When  the  spout  has  ceased  dripping,  counterpoise  the 
vessel  of  water  with  weights  in  the  other  scale-pan.  Place  a  floating 
body  on  the  water.  This  will  destroy  the  equilibrium,  but  water  will 
overflow  through  the  spout  until  the  equilibrium  is  restored.  This 
shows  that  the  floating  body  has  displaced  its  own  weight  of  water. 

Experiment  72.  — Place  a  fresh  egg  in  a  vessel  of  fresh  water ;  it  is 
a  little  heavier  than  the  water,  and  will  sink.  Place  it  in  salt  water  ; 
it  is  a  little  lighter  than  the  brine,  and  will  float.  Carefully  pour  the 
fresh  water  on  the  salt  water  in  a  tall,  narrow  vessel.  Place  the  egg 
in  the  water ;  it  will  descend  until  it  reaches  a  layer  of  the  liquid  with 
a  density  like  its  own,  and  there  it  will  float. 

154.  Floating  Bodies.  —  When  a  solid  is  immersed  in  a 
liquid  it  falls  under  one  of  three  cases,  according  as  the 
weight  of  the  solid  is  less  than,  equal  to,  or  greater  than 
that  of  the  displaced  liquid.  In  the  first  case,  the  buoyant 


166  SCHOOL  PHYSICS. 

effect  of  the  liquid  (§  153)  exceeds  the  weight  of  the 
body,  and  the  body  rises  to  the  surface  and  floats.  In 
the  second  case,  buoyancy  and  weight  are  equal  and  op- 
posite, and  their  resultant  is  zero ;  the  body  is  in  equi- 
librium in  any  part  of  the  liquid.  In  the  third  case, 
the  weight  exceeds  the  buoyancy,  and  the  body  sinks. 
But  in  any  case,  Archimedes'  principle  is  strictly  true. 
A  floating  body  is  only  partly  immersed,  and  the  volume 
of  liquid  displaced  by  it  is  only  a  fraction  of  its  own 
volume.  In  order  that  it  may  float  at  rest,  the  forces 
acting  upon  it  must  be  in  equilibrium  ;  i.e.,  the  upward 
and  the  downward  pressures  must  be  equal.  Conse- 
quently, the  law  of  flotation  is :  fA  floating  body  will  sink 
in  a  liquid  until  it  displaces  a  weight  of  the  liquid  equal  to 
its  own  weight.) 

(a)  Sometimes  a  heavy  substance  is  given  such  a  shape  that  it 
displaces  enough  of  a  lighter  fluid  to  float  thereon.  Thus,  an  iron 
kettle  or  an  iron  ship  floats  on  water,  although  iron  is  much  heavier 
than  water. 

(6)  Just  as  the  gravity  of  a  body  may  be  considered  as  acting  upon 
a  single  point  called  the  center  of  mass,  so  the  buoyant  effort  of  a 
fluid  may  be  considered  as  acting  upon  a  single  point  called  the 
center  of  buoyancy.  The  center  of  buoyancy  is  situated  at  the  center  of 
mass  of  the  displaced  fluid. 

CLASSROOM  EXERCISES. 

1.  How  much  weight  will  a  cubic  decimeter  of  iron  lose  when 
placed  in  water  ? 

2.  How  much  weight  will  it  lose  in  a  liquid  13.6  times  as  heavy 
as  water? 

3.  If  the  cubic  decimeter  of  iron  weighs  only  7,780  g.,  what  does 
your  answer  to  Exercise  2  signify  ? 

4.  How  much  weight  will  a  cubic  foot  of  stone  lose  in  water  ? 

5.  If  100  cu.  cm.  of  lead  weighs  1,135  g.,  what  will  it  weigh  in 
water? 


THE   MECHANICS   OF  LIQUIDS.  167 

6.  If  a  brass  ball  weighs  83.8  g.  in  air,  and  73.8  g.  in  water,  what  is  its 
volume  ? 

7.  A  cubical  vessel  20  cm.  on  an  edge  has  fitted  into  its  top  a  tube 
2  cm.  square  and  10  cm.  high.     Box  and  tube  being  filled  with  water, 
(a)  what  is  the  weight  of  the  water  ?    (6)  What  is  the  liquid  pressure 
on  the  bottom  of  the  vessel  ?     (c)  If  the  weight  and  pressure  differ, 
explain  the  difference. 

8.  In  Fig.  117,  the  line,  ABC,  represents 
the  surface  of  water  that  has  been  distorted 
from  its  level  condition.    Show  what  force 
acts  on  any  water  particle  in  the  distorted 
surface,  as  the  one  at  B,  and  moves  it  so 
that  the  surface  becomes  level.     At  what 


moment  does  that  force  vanish  ?  FIG.  117. 

155.  Density  and  Specific  Gravity.  —  The  density  of  a 
substance  is  its  mass  per  unit  of  volume.  The  specific 
gravity  of  a  substance  is  the  ratio  betiveen  the  weight  of  any 
volume  of  the  substance  and  the  weight  of  a  like  volume  of 
some  other  substance  taken  as  a  standard;  i.e.,  it  is  the 
ratio  of  its  density  to  that  of  some  standard  substance. 
For  solids  and  liquids,  the  standard  is  distilled  water  at 
its  temperature  of  maximum  density  (4°  C.  or  39.2°  F.); 
for  gases  and  vapors,  the  standard  is  hydrogen  or  air 
under  a  barometric  pressure  of  76  centimeters,  and  at 
the  temperature  of  0°  C. 

(a)  Since  the  weights  of  bodies  are  proportional  to  their  masses, 
specific  gravity  is  equivalent  to  relative  density.  The  term  "  density  " 
has  nearly  displaced  "  specific  gravity  "  in  scientific  works. 

(6)  To  illustrate,  in  the  simplest  way,  what  is  meant  by  density 
(i.e.,  specific  gravity),  suppose  that  1  cu.  cm.  of  marble  weighs  2.7  g. 
Since  1  cu.  cm.  of  water  weighs  1  g.,  the  marble  is  2.7  times  as  heavy 
as  water,  volume  for  volume.  In  shorter  phrase,  the  density  of  marble 
is  2.7.  To  avoid  the  difficulty  of  obtaining  just  a  unit  volume  of  the 
substance,  the  principle  of  Archimedes  is  utilized,  as  will  be  illus- 
trated. 


168 


SCHOOL  PHYSICS. 


156.    To   Find   the   Density  of   a   Solid   Heavier   than 
Water.  —  The   most    common   way   of    determining    the 

density  of  such  a  body, 
if  it  is  insoluble  in 
water,  is  to  find  its 
weight  in  air  (w) ;  find 
its  weight  when  im- 
mersed in  water  (w')\ 
divide  the  weight  in  air 
by  the  loss  of  weight  in 
water. 

w 


FIG.  118. 


D  = 


w  —  w 


(a)  This  method  is  illustrated  by  the  following  example  :  — 

(1)  Weight  of  the  solid  in  air  (w} 113.4    g. 

(2)  "        "     "      "      "  water         (w'} 79.14  g. 

(3)  "        "    equal    bulk  of  water  (to  —  to')  ...    34.26  g. 

(4)  Density  «    the  solid  (l)-(3)  . 3.31 

157.  The  Hydrometer.  —  Instruments  called  hydrometers 
are  made  for  the  more  convenient  determination  of  den- 
sities. There  are  hydrometers  of  constant  volume,  and 
hydrometers  of  constant  weight.  The  Nicholson  hydrom- 
eter of  constant  volume  is  a  hollow  cylinder  carrying 
at  its  lower  end  a  basket,  d,  heavy  enough  to  keep  the 
apparatus  upright  in  water.  At  the  top  of  the  cylinder 
is  a  vertical  rod  carrying  a  pan,  a,  for  holding  weights, 
etc.  The  whole  apparatus  must  be  lighter  than  water, 
so  that  a  certain  weight  (  W)  must  be  put  into  the  pan 
to  sink  the  apparatus  to  a  fixed  point  marked  on  the 
rod  (as  <?).  The  given  body,  which  must  weigh  less  than 
IF,  is  placed  in  the  pan,  and  enough  weights  (w)  added 


THE   MECHANICS  OF  LIQUIDS. 


169 


to  sink  the  point,  c,  to  the  water  line.     It  is  evident  that 
the  weight  of  the  given  body  is  W—  w.     The  given  body 


FIG.  119. 


is  now  taken  from  the  pan  and  placed  in  the  basket,  when 
additional  weights,  a?,  must  be  added  to  sink  the  point,  <?, 
to  the  water  line. 

D 


W- 


158.  To  Find  the  Density  of  a  Solid  Lighter  than  Water. 
—  Fasten  to  it  another  body  heavy  enough  to  sink  it  in 
water.     Find  the  loss  of  weight  for  the  combined  mass 
when  weighed  in  the  water.     Do  the  same  for  the  heavy 
body.     Subtract  the  loss  of  the  heavy  body  from  the  loss 
of  the  combined  mass.     Divide  the  weight  of  the  given 
body  by  this  difference. 

159.  To  Find  the  Density  of  a  Solid  Soluble  in  Water.  — 

Determine  the  density  of  the  given  solid  with  reference  to 
some  liquid,  the  density  (<?)  of  which  is  known,  and  in 
which  the  solid  is  not  soluble.  Multiply  the  result 


1TO 


SCHOOL   PHYSICS. 


obtained  by  any  of  the  processes  previously  described  by 
the  density  of  the  liquid  used. 

£  __     wd 
w  —  wf* 

160.  To  Find  the  Density  of  a  Liquid.  —  There  are  sev- 
eral methods  of  finding  the  density  of  a  liquid,  but  the 
principle  in  each  is  that  already  given. 

(a)  Four  of  these  methods  are  given  here ;  others  will  be  found  in 
the  Laboratory  Exercises. 

(1)  Weigh  a  flask  first,  empty ;  next,  full  of  water ;  then,  full  of 
the  given  liquid.     Subtract  the  weight  of  the  empty  flask  from  the 
other  two  weights ;  the  results  represent  the  weights  of  equal  volumes 
of  the  given  substance  and  of  the  standard.    Divide  as  before.   A  flask 
of  known  weight,  graduated  to  measure  100  or  1,000  grams  or  grains  of 
water,  is  called  a  specific-gravity  flask.     Its  use  avoids  the  first  and 
second  weighings  above  mentioned,  and  simplifies  the  work  of  division. 

(2)  Find  the  loss  of  weight  of  any  insoluble  solid  in  water  and  in 
the  given  liquid.     Divide  the  latter  loss  by  the  former.    A  solid  thus 
used  is  called  a  specific-gravity  bulb. 

(3)  The  Fahrenheit  hydrometer  of  constant  volume  is  made  of  glass, 

the  bulb  at  the  bottom  being  loaded 
with  mercury  or  shot.  Its  weight  (W) 
being  accurately  determined,  the  in- 
strument is  placed  in  water,  and  a 
weight  (w)  sufficient  to  sink  a  marked 
point  on  the  rod  to  the  water-line  is 
placed  in  the  pan.  The  weight  of  water 
displaced  by  the  instrument  =  W  +  w. 
The  hydrometer  is  then  removed,  wiped 
dry,  and  placed  in  the  given  liquid. 
A  weight  (ar)  sufficient  to  sink  the 
hydrometer  to  the  marked  point  is 
placed  in  the  pan. 

FIG.  120.  D  -  W  +  X 

W+w 

(4)  As  generally  made,  a  hydrometer   of  constant  weight   con- 
sists  of   a   glass    tube   near   the    bottom    of   which    are    two   bulbs. 


THE   MECHANICS   OF   LIQUIDS. 


171 


The  lower  and  smaller  bulb  is  loaded  with  mercury  or  shot.     The 

tube   and   upper  bulb   contain  air.     The   point  to  which  it  sinks 

when  placed  in  water  is  marked    zero.      The   tube    is   graduated, 

the  scale  being  arbitrary,  and  varying  with  the 

purpose  for  which   the  instrument  is  intended. 

Such   hydrometers    are    used  to  determine  the 

degree   of  concentration  of    certain  liquids,   as 

acids,   alcohols,   milk,    solutions  of    sugar,  etc. 

According   to   their   uses,   they  are   known    as 

acidometers,  alcoholometers,  lactometers,  saccharom- 

eters,  etc. 


FIG.  121. 


161.  To  Find  the  Density  of  a  Gas.  — 

The  density  of  an  aeriform  body  is  found 
by  comparing  the  weights  of  equal  vol- 
umes of  the  standard  (air  or  hydrogen) 
and  of  the  given  substance.    The  method 
is  strictly  analogous  to  that  first  given 
for  liquids.     The  determination  of  the  density  of  gases 
presents  many  practical  difficulties  which  cannot  be  con- 
sidered in  this  place. 

*. 

NOTE.  —  The  weight  of  any  solid  or  liquid,  in  grams  per  cubic 
centimeter,  represents  its  density. 

The  weight  of  a  cubic  foot  of  any  solid  or  liquid  is  equal  to  62.421 
pounds  avoirdupois  multiplied  by  its  density. 

The  weight  of  a  cubic  centimeter  of  any  solid  or  liquid  is  equal  to 
1  gram  multiplied  by  its  density. 

The  weight  of  a  liter  of  any  liquid  or  a  cubic  decimeter  of  any  solid 
is  equal  to  1  kilogram  multiplied  by  its  density. 

162.  Water  Power.  —  An  elevated  body  of  water  is  a 
storehouse   of   potential   energy.     As  the  water  runs  to 
a  lower  level,  it  may  be  made  to  turn  a  wheel,  and  thus 
to  move  machinery,  etc.,  a  good  illustration  of  the  con- 
version of  potential  into  kinetic  energy. 

"   (a)  Water-wheels  are  of  different  kinds,  their  relative  advantages 
depending  upon  the  nature  of  the  water-supply  and  of  the  work  to  be 


172 


SCHOOL  PHYSICS. 


done.  In  the  overshot  wheel  (Fig.  122),  the  water  falls  into  buckets 
at  the  top,  and  by  its  weight,  aided  by  the  force  of  the  current,  turns 
the  wheel.  Such  wheels  have  been  made  nearly  100  feet  in  diameter. 


FIG.  122. 

The  little  water  that  they  need  must  have  a  considerable  fall.  In  the 
breast  wheel,  the  water  is  received  at  or  near  the  level  of  the  axis ; 
thus  the  weight  of  the  water  and  the  force  of  the  current  are  turned 
to  account.  In  the  undershot  wheel,  the  water  acts  upon  a  few  float- 


FIQ.  123. 

boards  at  the  bottom,  the  force  of  the  current  turning  the  wheel.  The 
most  efficient  form  of  water-wheel  is  the  turbine,  one  form  of  which  is 
shown  in  Fig.  123.  The  wheel,  B,  and  the  inclosing  case,  D,  are  placed 


THE   MECHANICS   OF   LIQUIDS.  178 

on  the  floor  of  a  penstock  wholly  submerged  in  water  under  the 
pressure  of  a  considerable  head.  The  water  enters,  as  shown  by  the 
arrows,  through  openings  in  D,  which  are  so  constructed  that  it  strikes 
the  buckets  of  B  in  the  direction  of  greatest  efficiency.  After  leaving 
the  buckets,  the  "  dead  water "  escapes  from  the  central  part  of  the 
wheel,  sometimes  by  a  vertical  draft-tube.  The  weight  of  the  water 
in  this  tube  increases  the  velocity  with  which  the  water  strikes  the 
buckets.  A  central  shaft,  A,  is  carried  by  the  wheel,  and  communi- 
cates its  motion  to  the  machinery  above.  The  wheel  itself  rests  upon 
a  central  pivot  carried  by  cross-arms  from  the  bottom  of  the  outer 
case.  The  case,  Z>,  is  covered  with  a  top,  !T,  which  protects  the  wheel 
from  the  vertical  pressure  of  the  water. 


CLASSROOM  EXERCISES. 

NOTE.  —  Be  on  the  alert  to  recognize  Archimedes'  Principle  in  dis- 
guise.    Consider  the  weight  of  water  62^  pounds  per  cubic  foot. 

1.  What  is  the  density  of  a  body  that  floats  with  half  of  its  vol- 
ume under  water  ? 

2.  Assuming  the  density  of  aluminium  to  be  2.6,  determine  the 
weight  of  an  aluminium  sphere  25  cm.  in  diameter. 

3.  A  piece  of  metal  weighing  52.35  g.  in  air  is  placed  in  a  cup  filled 
with  water.     The  overflowing  water  weighs  5  g.     What  is  the  density 
of  the  metal  ? 

4.  A  solid  weighing  695  g.  in  air  loses  83  g.  when  weighed  in  water, 
(a)  What  is  its  density  ?     (b)  How  much  would  it  weigh  in  alcohol 
that  has  a  density  of  0.792  ? 

5.  A  1,000-grain  bottle  holds  708  grains  of  benzoline.     Find  the 
density  of  the  benzoline. 

6.  A  solid  that  weighs  2.4554  ounces  in  air,  weighs  only  2.0778 
ounces  in  water.     Find  its  density. 

7.  A  specimen  of  gold  that  weighs  4.6764  g.  In  air,  loses  0.2447  g. 
weight  when  weighed  in  water.     Find  its  density. 

8.  A  ball  weighing  970  grains,  weighs  in  water  895  grains,  in  alco- 
hol 910  grains.     Find  the  density  of  the  alcohol. 

9.  A  body  loses  25  grains  in  water,  23  grains  in  oil,  and  19  grains 
in  alcohol.     Required  the  density  of  the  oil  and  of  the  alcohol. 

10.  A  body  weighing  1,536  g.,  weighs  in  water  1,283  g.     What  is 
its  density? 


174  SCHOOL  PHYSICS. 

11.  Calculate    the    density    of    sea    water    from    the    following 
data :  — 

Weight  of  bottle  empty 3.5305  g. 

"  "       filled  with  distilled  water  .  .  7.6722  g. 

"  "          "  sea  "       .  .  7.7849  g. 

12.  Determine  the  density  of  a  piece  of  wood  from  the  following 
data :  weight  of  wood  in  air,  4  g. ;  weight  of  sinker,  10  g. ;  weight  of 
wood  and  sinker  under  water,  8.5  g. ;  density  of  sinker,  10.5. 

13.  A  piece  of  a  certain  metal  weighs  3.7395  g.  in  air;  1.5780  g. 
in  water;  2.2896  g.  in  another  liquid.     Calculate  the  densities. of  the 
metal  and  of  the  unknown  liquid. 

14.  Find  the  density  of  a  piece  of  glass,  a  fragment  of  which  weighs 
2,160  grains  in  air,  and  1,51 1£  grains  in  water. 

15.  A  lump  of  ice  weighing  8  pounds  is  fastened  to  16  pounds  of 
lead.     In  water,  the  lead  alone  weighs  14.6  pounds,  while  the  lead  and 
ice  weigh  13.712  pounds.     Find  the  density  of  the  ice. 

16.  A  piece  of  lead  weighing  600  g.  in  air  weighs  545  g.  in  water, 
and  557  g.  in  alcohol.    Find  (a)  the  density  of  the  lead ;  (&)  the  density 
of  the  alcohol ;  (c)  the  volume  of  the  lead. 

17.  A  person  can  just  lift  a  300-pound  stone  in  the  water.     What 
is  his  lifting  capacity  in  the  air  (density  of  the  stone,  2.5)  ? 

18.  A  liter  flask  holds  870  g.  of  turpentine.     Required  the  density 
of  the  turpentine. 

[In  the  next  two  exercises,  the  weight  of  the  empty  flask  is  not 
taken  into  account.] 

19.  A  liter  flask  containing  675  g.  of  water  had  its  remaining  space 
filled  with  fragments  of  a  mineral,  and  was  found  to  weigh  1,487.5  g. 
Required  the  density  of  the  mineral. 

20.  A  liter  flask  was  four-fifths  filled  with  water;  the  remaining 
space  being  filled  with  sand,  the  weight  was  found  to  be  1,350  g. 
Required  the  density  of  the  sand. 

21.  A  weight  of  1,000  grains  will  sink  a  certain  Nicholson  hydrom- 
eter to  a  mark  on  the  rod  carrying  the  pan.     A  piece  of  brass  plus  40 
grains  will  sink  it  to  the  same  mark.     When  the  brass  is  taken  from 
the  pan  and  placed  in  the  basket,  it  requires  160  grains  in  the  pan  to 
sink  the  hydrometer  to  the  same  mark  on  the  rod.     Find  the  density 
of  the  brass. 

22.  A  Fahrenheit  hydrometer,  which  weighs  2,000  grains,  re'quires 
1,000  grains  in  the  pan  to  sink  it  to  a  certain  depth  in  water.  '  It  re- 


THE    MECHANICS   OF   LIQUIDS.  175 

quires  3,400  grains  in  the  pan  to  sink  it  to  the  same  depth  in  sulphuric 
acid.    Find  the  density  of  the  acid. 

23.  A  certain  body  weighs  just  10  g.    It  is  placed  in  one  of  the 
scale-pans  of  a  balance,  together  with  a  flask  full  of  pure  water.     The 
given  body   and  the  filled  flask  are  counterpoised  with  shot  in  the 
other  scale-pan.      The  flask  is  removed,  and  the  given  body  placed 
therein,  thus  displacing  some  of  the  water.     The  flask,  being  still 
quite  full,  is  carefully  wiped  and  returned  to  the  scale-pan,  when  it  is 
found  that  there  is  not  equilibrium.     To  restore  the  equilibrium,  it 
is  necessary  to  place  2.5  g.  with  the  flask.     Find  the  density  of  the 
given  body. 

24.  What  would  a  cubic  foot  of  coal  (density,  2.4)  weigh  in  a  solu- 
tion of  potash  (density,  1.2)  ? 

25.  500  cu.  cm.  of  iron  (density,  7.8)  floats  on  mercury.     With 
what  force  is  it  buoyed  up? 

26.  A  piece  of  cork  weighing  2.3  g.  was  attached  to  a  piece  of  iron 
weighing  38.9  g.     Both  were  found  to  weigh  in  water  26.2  g.,  the  iron 
alone  weighing  33.9  g.  in  water.     Required  the  density  of  the  cork. 

27.  A  piece  of  wood  weighing  300  grains  has  tied  to  it  a  piece  of 
lead  weighing  600  grains ;  together  they  weigh  in  water  472.5  grains. 
The  density  of  lead  being  11.35,  (a)  what  does  the  lead  weigh  in 
water?     (&)  What  is  the  density  of  the  wood? 

28.  A  Fahrenheit  hydrometer  weighs  618  grains.     It  requires  93 
grains  in  the  pan  to  sink  it  to  a  certain  mark  on  the  stem.     When 
wiped  dry  and  placed  in  olive  oil,  it  requires  only  31  grains  to  sink 
it  to  the  same  mark.     Find  the  density  of  the  oil. 

29.  A  platinum  ball  weighs  330  g.  in  air,  315  g.  in  water,  and  303  g. 
in  sulphuric  acid.    Find  (a)  the  density  of  the  ball ;  (&)  the  density 
of  the  acid ;  (c)  the  volume  of  the  ball. 

30.  A  hollow  ball  of  iron  weighs  1  Kg.    What  must  be  its  least 
volume  to  float  on  water  ? 

31.  A  body  whose  density  is  2.8  weighs  37  g.    Required  its  weight 
in  water. 


176  SCHOOL  PHYSICS. 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  piece  of  rock-salt ;  naphtha ;  pine  rod, 
loaded  and  graduated  as  described  below ;  rectangular  prism  of  hard 
wood ;  piece  of  brimstone ;  bottle  with  ground-glass  stopper ;  kerosene ; 
wooden  cylinder  and  support ;  Y-tube ;  pinchcock. 

1.  Determine  the  density  of  two  solids  heavier  than  water,  the 
solids  being  supplied  by  the  teacher. 

2.  Determine  the  density  of  a  solid  lighter  than  water. 

3.  Determine  the  density  of  an  unknown  liquid  without  using  a 
specific-gravity  flask  or  a  hydrometer. 

4.  Rock-salt  is  soluble  in  water,  and  insoluble  in  naphtha.     Deter- 
mine the  density  of  a  specimen  of  rock-salt. 

5.  Determine  the  density  of  a  liquid,  using  a  specific-gravity  bulb. 

6.  Redetermine  the  density  of  one  of  the  solids  used  in  Exercise  1, 
using  a  Nicholson  hydrometer. 

7.  Get  a  rectangular  block  of  hard  wood  about  5x6x7  centime- 
ters.    The  exact  dimensions  are  not  essential.     Weigh  the  block  on  a 
spring-balance   suspended   from   some    firm    support    (not    held   in 
the  hand).     Measure  the  dimensions  of  the  block  as  accurately  as 
possible,  and  compute  its  volume  in  cubic  centimeters  and  cubic  inches. 
Determine  the  weight  of  the  block  in  grams  per  cubic  centimeter,  and 
in  ounces  per  cubic  inch. 

8.  Provide  a  water-proofed  wooden  cylinder  about  1  cm.  in  diam- 
eter and  about  20  cm.  long,  and  a  support  for  holding  the  cylinder 
upright  in  the  water  in  such  a  way  that  it  may  easily  move  up  and 
down  without  tipping  much  from  a  vertical  position.     Accurately 
measure  the  length  of  the  cylinder.     When  the  cylinder  is  floating 
upright  in  water,  joggle  it  a  few  times,  and  see  that  it  comes  to  rest 
each  time  at  the  same  depth.     Accurately  measure  the  length  of  the 
submerged  part  of  the  cylinder,  and  from  the  two  measurements,  com- 
pute the  density  of  the  cylinder. 

9.  Make  a  rod  of  white  pine  or  other  light  wood,  just  1  cm.  square 
and  about  30  cm.  long.     Graduate  one  side  of  the  rod  to  millimeters, 
with  the  zero  of  the  scale  at  the  loaded  end.     In  one  end,  bore  a  hole, 
and  pound  in  enough  sheet  lead  to  make  the  rod  stand  on  end  when 
floated  in  water  and  with  about  half  of  it  immersed.     Fill  the  rest  of 
the  cavity  with  putty,  and  dip  the  rod  into  hot  paraffme.     Place  the 
rod  in  water,  and  read  from  the  scale  the  depth  to  which  it  sinks. 


THE   MECHANICS   OF   LIQUIDS.  177 

Using  it  as  a  hydrometer  of  constant  weight,  determine  the  density 
of  alcohol  and  of  a  20-per-cent  solution  of  common  salt. 

10.  Paste  a  strip  of  writing  paper  around  the  upper  end  of  the  rod 
used  in  Exercise  9,  one  edge  of  the  paper  overlapping  the  end  of  the 
stick  so  as  to  make  a  small  cup.     Float  the  rod  as  before,  and  place 
enough  shot  or  sand  in  the  cup  to  bring  one  of  the  graduations  ex- 
actly to  the  water-level.      Add  successively  weights  of  1  g.,  2  g.,  3  g., 
etc.,  and  at  each  addition,  note  how  much  the  rod  sinks.     Record  the 
teachings  of  the  experiment. 

11.  Fill  the  tin  can  used  in  Experiment  69,  until  water  overflows 
through  the  spout.     Weigh  a  small  beaker,  and  place  it  under,  the 
spout.     Weigh  a  piece  of^  roll  sulphur  (brimstone)  about  5  cm.  long, 
suspend  it  by  a  fine  thread,  and  lower  it  into  the  water  in  the  tin  can, 
catching  in  the  beaker  every  drop  of  water  that  overflows.     Weigh 
the  beaker  with  its  liquid  contents,  and  by  subtraction  find  the  weight 
of  water  it  contains.     Suspend  the  sulphur  by  the  thread  from  the 
scale-pan,  and  weigh  it  in  water.     Record  your  data  as  follows :  — 

(a)  Weight  of  sulphur  in  air  =  ? 

(6)  Weight  of  beaker  =  ? 

(c)  Weight  of  beaker  and  water  =  ? 

(rf)  Weight  of  displaced  water  (c-Z>)  =? 

(e)  Weight  of  sulphur  in  water  =  V 

(/)  Loss  of  weight  in  water  (a  —  e)  =  ? 

Compare  (e?)  with  (/),  and  record  the  fact  thus  indicated.     From  the 
recorded  data,  determine  the  density  of  the  sulphur. 

12.  Provide  a  bottle  that  will  hold  two  or  three  ounces  of  water, 
and  that  has  a  ground-glass  stopper ;  a  thread  with  which  to  suspend 
the  bottle  ;  a  cloth  with  which  to  wipe  the  bottle  ;  a  delicate  spring- 
balance  ;  water ;  kerosene.     Without  any  other  apparatus  or  supplies, 
determine  the  density  of  the  kerosene. 

13.  Fill  a  bottle  like  that  used  in  Exercise  12  with  water,  and  put 
the  stopper  firmly  into  place.     Without  removing  the  stopper  or  add- 
ing to  your  material,  determine  the  density  of  the  kerosene. 

14.  Get  a  glass  U-tube  with  an  internal  diameter  of  8  or  10  mm. 
and  having  arms  that  are  close  together  and  about  50  cm.  long  (see 
Fig.  110) ;  a  meter  stick  graduated  to  millimeters ;  a  small  funnel  for 
pouring  liquids  into  the  U-tube ;  some  support  that  will  hold  the 
U-tube   upright;    water;   kerosene.     Without    additional    material, 
determine  the  density  of  the  kerosene. 

12 


178  SCHOOL   PHYSICS. 

15.  Get  a  lead  or  glass  Y-tube  (i.e.,  a  three-way  tube),  each  arm  of 
which  has  a  length  of  about  5  cm.,  and  an  internal  diameter  of  about 

5  mm. ;  two  pieces  of  glass  tubing  each  having  an  ex- 
ternal diameter  about  equal  to  that  of  the  Y-tu.be,  and 
a  length  of  50  cm. ;  two  pieces  of  rubber  tubing  about 
5  cm.  long,  for  connecting  the  two  straight  tubes  to  the 
Y-tube ;  a  piece  of  rubber  tubing  about  10  cm.  long  to 
attach  to  the  other  arm  of  the  Y-tube,  and  a  pinchcock 
IG'  '  (see  Chemistry,  Appendix  20)  or  other  device  for  clos- 
ing the  free  end  of  the  tube;  the 
meter  stick  used  in  Exercise  14 ; 
two  tumblers ;  water ;  kerosene. 
Without  additional  material,  deter- 
mine the  density  of  kerosene.  Make 
any  necessary  corrections  for  capil- 
lary action.  Remember  that  you 
can  easily  suck  air  from  or  through 
the  apparatus. 

16.  Using   the   apparatus   shown 
in  Fig.  110,  and  a  meter  stick,  de- 
termine the  density  of  mercury. 

17.  Wind  closely  10  m.  of  No.  22 
spring-brass  wire  upon  a  rod  about 
3  cm.  in  diameter,  and  suspend  the 
spiral  thus  formed  in  front  of  a  ver- 
tical meter  stick  or  other  scale,  as 
shown  in  Fig.  125.     To  the  lower 
end  of  the  spring,  the  extremity  of 
the  wire  having  been  bent  into  a 
horizontal  index,  attach  two  small 
scale-pans     arranged    so    that    one 
shall  be  about   10  cm.    below    the 
other.     Place  a  glass  of  water  upon 
an  adjustable  stand  or  easily  mov- 
able blocks  so  that  the  lower  pan 
may  be  kept   immersed   while   the 
upper  pan  is  always  above  the  water. 
In  the  upper  pan,  place  a  small  solid 

that  will  sink  in  water,  and  note  the  elongation  of  the  spring  as  in- 
dicated by  the  movement  of  the  index  over  the  scale,  lowering  the 


THE    MECHANICS   OF   GASES. 

dish  of  water  as  may  be  necessary  to  keep  the  lower  pan  submerged 
and  freely  suspended.  Then  place  the  solid  in  the  lower  pan,  and 
similarly  weigh  it  in  water.  Determine  the  density  of  the  solid. 

18.  Place  a  1-gram  weight  in  the  upper  pan  of  the  Jolly  balance 
described  in   Exercise  17,  and  note  the   elongation  of  the  spring. 
Assuming  that  the  spring  will  stretch  proportionally  for  other  loads, 
obtain  in  grams  the  two  weights  of  another  small  solid  that  will  sink 
in  water,  and  determine  its  density. 

19.  Place  a  cork  in  the  upper  pan  of  the  Jolly  balance,  and  a  sinker 
in  the  lower  pan,  and  weigh  them.     Fasten  the  sinker  to  the  cork, 
place  both  in  the  lower  pan,  and  weigh  them.     Determine  the  density 
of  the  cork. 

20.  Remove  both  pans  from  the  Jolly  balance,  and  suspend  the 
glass  stopper  of  a  bottle  from  the  lower  end  of  the  spring.     With 
this  apparatus,  determine  the  density  of  kerosene. 


VIII.    THE   MECHANICS   OF   GASES. 

163.  Pneumatics  is  the  branch  of  physics  that  treats  of 
the  mechanical  properties  of  gases,  and  describes  the  ma- 
chines that  depend  for  their  action  chiefly  on  the  pressure 
and  elasticity  of  air. 

(a)  As  water  was  taken  as  the  type  of  liquids,  so  atmospheric  air 
will  be  taken  as  the  type  of  gases.  All  statements  made  in  Section 
VII.  concerning  fluids,  apply  to  gases  as  well  as  to  liquids. 

NOTE.  —  It  is  taken  for  granted  that  the  school  has  an  air-pump, 
an  instrument  that  will  soon  be  described,  and  the  simpler  pieces  of 
apparatus  that  generally  accompany  it. 

Weight  of  Air. 

Experiment  73.  — On  a  delicate  balance,  carefully  weigh  a  thin 
glass  or  metal  vessel  that  will  hold  several  liters,  and  that  may  be 
closed  by  a  stopcock.  Pump  the  air  from  the  vessel,  close  the  stop- 
cock, remove  the  vessel  from  the  pump  and  carefully  weigh  it  again. 


180 


SCHOOL   PHYSICS. 


FIG.  120. 


Its  loss  of  weight  measures  the  weight  of  the  air  removed.  If  more 
convenient,  the  following  may  be  substituted  for  the  foregoing:  — 
Into  a  half-liter  Florence  flask,  put  about  100 
cu.  cm.  of  water.  Place  the  flask  on  a  sand-bath 
and  boil  the  water.  The  steam  will  expel  the  air 
from  the  flask.  After  the  boiling  has  continued 
for  some  time,  remove  the  lamp,  and,  when  the 
boiling  has  ceased,  loosely  cork  the  flask.  Cool 
the  upper  part  of  the  flask  by  putting  a  wet  cloth 
around  it ;  the  water  will  boil  again.  Then  tightly 
close  the  flask  with  a  rubber  stopper.  When  the 
flask  has  cooled  to  the  temperature  of  the  room, 
shake  it.  The  peculiar  "  water-hammer  "  sound  of 
the  water  indicates  a  good  vacuum  in  the  flask. 
Weigh  the  flask  and  its  contents.  Loosen  the 
cork  and  weigh  again.  The  increase  of  weight  is  the  weight  of 
the  air  admitted  to  the  flask.  Subtract  the  volume  of  the  water  from 
the  capacity  of  the  flask  to  find  the  volume  of  the  air  thus  weighed 
and  compute  the  weight  of  the  air  per  cubic  centimeter.  Record  the 
readings  of  the  thermometer  and  barometer  at  the  time  and  place 
of  the  experiment. 

Experiment  74.  —  Draw  out  a  piece  of  glass  tubing  to  a  jet,  and 
push  it  through  a  perforation  in  a  cork  that  snugly  fits  a  bottle.  Slip 
a  short  piece  of  snugly  fitting  rubber  tubing  over  the 
outer  end  of  the  glass  tubing,  and  insert  the  cork  so 
that  the  jet  shall  project  into  the  bottle.  Remove  by 
suction  as  much  air  as  possi- 
ble from  the  bottle,  pinch  the 
rubber  tubing  tightly,  place  it 
under  water,  and  remove  the 
pressure.  Something  will  force 
water  into  the  bottle,  forming 
the  "  fountain  in  vacuo,"  as 
shown  in  Fig.  127. 


FIG.  127. 


Experiment  75.  —  Fill  a 
tumbler  with  water,  place  a 
slip  of  thick  paper  over  its 


FIG.  128. 


mouth  and  hold  it  there  while  the  tumbler  is  inverted ;  the  water  will 
be  supported  when  the  hand  is  removed  from  the  card. 


THE   MECHANICS  OF   GASES.  181 

Experiment  76.  —  Over  the  upper  end  of  a  cylindrical  receiver,  tie 
tightly  a  wet  bladder  or  sheet  of  writing  paper  and  allow  it  to  dry. 
Then  exhaust  the  air.     The  bladder  will  be 
forced  inward,  bursting  with  a  loud  noise. 
Replace   the   bladder  with  a  thin  sheet  of 
india-rubber.      Exhaust  the  air.     The  rub- 
ber sheet  will  be  pressed  inward,  and  nearly 
cover  the  inner  surface  of  the  receiver. 


Experiment  77.  —  The  Magdeburg  hem- 
ispheres are  accurately  fitting,  metallic 
vessels,  generally  three  or  four  inches  in 
diameter.  Their  edges  are  provided  with 
projecting  lips,  and  fit  one  another  air-tight ;  FiaTl29. 

the  lips  prevent  sidewise  slipping.     Grease 

the  edges  to  make  more  sure  of  a  tight  joint,  fit  the  hemispheres 
to  each  other,  and  exhaust  the  air  with  a  pump.  Close  the  stop- 
cock, remove  the  hemispheres  from 
the  pump,  attach  the  second  handle, 
and,  holding  the  hemispheres  in  dif- 
ferent positions,  try  to  pull  them 
apart.  When  you  are  sure  that  the 
pressure  that  holds  them  together 
is  exerted  in  all  directions,  place 
them  under  the  receiver  (i.e.,  the 
bell-glass)  of  the  air-pump,  and  ex- 
haust the  air  from  around  them. 
The  pressure  seems  to  be  removed, 
for  the  hemispheres  fall  apart  of 
their  own  weight. 

Experiment  78.  —  Connect  the  lamp- 
chimney  apparatus  used  in  Experi- 
ment 59  by  a  thick-walled  rubber 
tube,  and  partly  exhaust  the  air  with 

FIG.  130.  the  air-pump  or  by  suction.     Hold 

the  chimney  in   different   positions, 

and  notice  that  the  pressure  that  pushes  in  the  rubber  diaphragm  is 
exerted  equally  in  all  directions.  Any  change  of  pressure  will  be 
shown  by  a  change  in  the  form  of  the  rubber  cup. 


182 


SCHOOL  PHYSICS. 


164.  The  Air.  —  These  experiments  show  that  air  has 
weight,  that  it  exerts  great  pressure  at  the  surface  of  the 
earth,  and  that  this  pressure  is  transmitted  equally  in  all 
directions,  in  accord  with  Pascal's  law.  Under  ordinary 
atmospheric  conditions,  a  liter  of  air  weighs  about  1.3 
grams  ;  a  cubic  foot  weighs  about  an  ounce  and  a  quarter. 
As  the  atmospheric  pressure  is  due  to  the  weight  of  the 
overlying  air,  it  follows  that  atmospheric  pressure  must 
decrease  as  we  ascend  from  the  sea-level. 


Atmospheric  Pressure. 

Experiment  79.  —  Into  one  end  of  a  piece  of  stout  glass  tubing  about 
1  m.  long,  and  with  a  bore  of  about  1  cm.,  closely  press  a  good  cork  or 
rubber  stopper.  Fill  the  tube  with  water ;  close  the  open  end  with 
the  forefinger ;  invert  the  tube  over  the  water-bath,  and,  when  the 

end  is  under  water,  remove  the 
finger.  Note  whether  the  water 
falls  away  from  the  corked  encl 
of  the  tube.  Loosen  or  remove 
the  cork,  and  note  the  result. 

Experiment  80.  —  Fill  with 
mercury  a  stout  glass  tube 
closed  at  one  end  and  about 
50  cm.  long ;  a  long  "  ignition 
tube "  will  answer.  Invert  it 
at  the  mercury-bath  as  shown 
in  Fig.  131.  Note  whether  the 
mercury  falls  away  from  the 
closed  end  of  the  tube. 

Experiment  81.  —  Select  a 
stout  glass  tube  about  80  cm. 

FlG  131  long,  several  millimeters  in  in- 

ternal diameter,  and  closed  at 

one  end.     Twist  a  piece  of  paper  into  the  shape  of  a  hollow  cone,  and, 
using  it  as  a  funnel,  fill  the  tube  with  mercury.     With  an  iron  wire, 


THE   MECHANICS   OF   GASES.  183 

remove  any  air-bubbles  that  you  see  in  the  tube.  Close  the  open 
end  with  the  finger,  and  invert  the  tube  at  the  mercury-bath,  as  shown 
in  Fig.  131.  When  the  finger  is  removed,  the  mercury  falls  away 
from  the  upper  end  of  the  tube,  and  finally  comes  to  rest  at  a  height 
of  about  30  inches  (or  76  cm.)  above  the  level  of  the  mercury  in  the 
bath,  leaving  a  vacuum  at  the  upper  end  of  the  tube.  This  historical 
experiment  was  first  performed  in  1643,  by  Torricelli,  Galileo's  pupil. 
If  the  tube  is  supported  upright,  the  height  of  the  sustained  mer- 
cury column  may  be  found  to  vary  from  day  to  day.  If  it  is 
placed  under  a  tall  bell-glass  and  the  air  exhausted,  the  column 
will  fall  as  the  atmospheric  pressure  on  the  surface  of  the  mercury 
decreases. 

Experiment  82.  —  Modify  the  last  experiment  by  selecting  a  tube 
open  at  both  ends.  Thoroughly  soak  in  water  such  a  membrane  as 
comes  tied  over  the  stoppers  of  perfumery  bottles,  and  tie  it  tightly 
over  One  end  of  the  tube.  When  the  membrane  is  thoroughly  dry, 
fill  the  tube  with  mercury,  and  invert  it  at  the  mercury-bath  as  before. 
After  measuring  the  height  of  the  supported  liquid  column,  prick  a 
pinhole  through  the  membrane,  and  notice  what  takes  place. 

165.  Atmospheric  Pressure.  —  In  spite  of  the  tendency 
of  liquids  to  seek  their  level,  we  see  that  something  sup- 
ports a  liquid  column  of  great  weight  in  the  Torricellian 
tube.  The  removal  of  the  air  from  the  surface  of  the 
mercury  in  the  bath  shows  that  the  pressure  of  the  atmos- 
phere is  this  supporting  force.  Since  the  size  of  the  tube 
will  not  affect  the  height  of  the  column,  we  may  assume 
that  the  tube  has  a  cross-section  of  one  square  centimeter. 
Then  the  supported  mercury  will  measure  76  cu.  cm.  As 
the  density  of  mercury  is  13.596,  this  quantity  of  mercury 
will  weigh  13.596  times  76  grams.  The  weight  thus 
sustained  shows  that  the  atmospheric  pressure  at  the  sea- 
level  is  approximately  1,033.3  e^raflis  per  square  centimeter,  or 
14.7  pounds  per  square  inch.  For  rough  work  or  "  in  round 
numbers,"  it  is  often  said  that  this  pressure,  which  is  called 


184 


SCHOOL  PHYSICS. 


an  atmosphere^  is  a  kilogram   per  square  centimeter,  or 
fifteen  pounds  per  square  inch. 

(a)  Pascal  carried  a  Torricellian  tube  to  the  top  of  a  mountain,  and 
there  found  that  the  mercury  column  was  three  inches  shorter,  showing 
that,  as  the  weight  of  the  atmospheric  column  diminishes,  the  counter- 
balanced column  of  mercury  also  diminishes.  He  then  took  a  tube 
40  feet  long,  and  closed  at  one  end.  Having  filled  it  with  water,  he 
inverted  it  over  a  water-bath.  The  water  in  the  tube  came  to  rest  at 
a  height  of  34  feet.  The  weights  of  the  two  columns  were  equal. 
Experiments  with  still  other  liquids  gave  corresponding  results,  all  of 
which  strengthened  the  theory  that  the  supporting  force  is  atmos- 
pheric pressure,  and  left  no  doubt  as  to  its  correctness. 

(6)  Since  mercury  is  more  than  ten  thousand  times  as  heavy,  bulk 
for  bulk,  as  air  under  the  ordinary  conditions  of  temperature  and 
atmospheric  pressure,  a  mercury  column  about  76  cm.  (or  30  inches) 
tall  is  able  to  counterbalance  an  air  column  of  equal  cross-section 
reaching  from  the  bottom  to  the  top  of  our  atmosphere. 

166.  The  Barometer. — A  Torricellian  tube,  firmly  fixed 
to  an  upright  support  and  properly  graduated, 
constitutes  a  mercurial  barometer.  The  zero  of 
the  scale  is  at  the  surface  of  the  mercury  in  the 
cistern. 

(a)  When  scientific  accuracy  is  required,  the  cistern  of 
the  barometer  is  made  with  a  flexible  leather  bottom 
that  can  be  raised  or  lowered  by  a  screw  until  the 
surface  of  the  mercury  just  touches  the  point  of  an  in- 
dex, with  which  the  zero  of  the  scale  coincides.  For 
the  more  accurate  reading  of  the  scale,  some  instruments 
are  provided  with  verniers.  In  every  case,  the  extreme 
height  of  the  convex  surface  of  the  mercury  should  be 
taken,  and,  if  the  scale  has  no  vernier,  the  divisions  of 
the  scale  should  be  subdivided  by  the  eye  as  accurately 
as  possible.  The  height  of  the  barometer  is,  in  such 
cases,  corrected  for  temperature,  for  variations  of  graV- 
ity,  for  capillarity,  for  expansion  of  the  scale,  for  eleva- 
tion above  sea-level,  etc. 
FIG.  132. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 


THE   MECHANICS  OF   GASES. 


185 


(6)  The  aneroid  barometer  is  an  easily  portable  instrument,  and 
avoids  the  use  of  any  liquid.  It  consists  of  a  circular  metallic  box, 
exhausted  of  air,  the  corrugated  dia- 
phragm of  which  is  held  in  a  state  of 
tension  by  springs.  Varying  atmos- 
pheric pressures  cause  movements  of  the 
diaphragm.  These  movements,  being 
multiplied  by  delicate  levers  and  a  fine 
chain  wound  around  a  pinion,  move  the 
index  pointer  over  a  graduated  scale. 
Such  barometers  are  made  so  delicate 
that  they  show  a  difference  in  atmos- 
pheric pressure  when  transferred  from 
an  ordinary  table  to  the  floor.  Their 
very  delicacy  involves  the  necessity  for 
careful  usage  or  frequent  repairs. 

FIG.  133. 
167.     Barometric    Variations.  — 

Observation  shows  frequent  variations  in  the  barometric 
readings.  Some  slight  changes  are  found  to  be  periodic, 
but  the  greater  changes  follow  no  known  law.  The  util- 
ity of  a  barometer  depends  largely  upon  the  fact  that  these 
irregular  variations  correspond  to  changes  in  the  pressure  of 
the  air  column  that  rests  on  the  surface  of  the  mercury  in 
the  cistern,  and,  therefore,  signal  coming  meteorological 
changes. 

0)  The  falling  of  the  mercury  generally  indicates  the  approach  of 
foul  weather;  a  sudden  .fall  denotes  the  coming  of  a  storm.  The 
rising  of  the  mercury  indicates  the  approach  of  fair  weather  or  the 
"  clearing  up  "  of  a  storm. 

(6)  Sometimes  the  "barometer  falls"  and  the  looked-for  storm 
does  not  appear.  In  such  a  case,  it  should  be  remembered  that  the 
barometer  announced  only  a  diminution  of  atmospheric  pressure,  and 
that  we,  influenced  by  experience,  inferred  the  coming  of  a  storm. 
Barometric  declarations  are  reliable;  inferences  from  those  declara- 
tions are  subject  to  error. 

(c)  The  barometer  is  also  used  for  the  approximate  determination 
-  of  altitudes  above  sea-level. 


186  SCHOOL  PHYSICS. 

CLASSROOM  EXERCISES. 

1.  Give  the  pressure  of  the  air  upon  a  man  the  surface  of  whose 
body  is  20  square  feet. 

2.  A  soap-bubble  has  a  diameter  of  4  inches.     Give  the  pressure  of 
the  air  upon  it. 

3.  What  is  the  weight  of  the  air  in  a  room  30  by  20  by  10  feet? 

4.  What  will  be  the  total  pressure  of  the  atmosphere  on  a  deci- 
meter cube  of  wood  when  the  barometer  stands  at  760  mm.? 

5.  How  much  weight  does  a  cubic  foot  of  wood  lose  when  weighed 
in  air? 

6.  (a)  What  is  the  pressure  on  the  upper  surface  of  a  Saratoga 
trunk  1\  by  3£  feet?     (b)  How  happens  it  that  the  owner  can  open 
the  trunk  ? 

7.  (a)  What  effect  would  it  have  Upon  the  height  of  the  barometer 
column  if  the  barometer  tube  was  enlarged  until  it  had  a  sectional 
area  of  1  sq.  cm.  ?     (6)  Assuming  that  the  density  of  mercury  is  13.6, 
and  that  the  barometer  stands  at  760  mm.,  what  is  the  atmospheric 
pressure  per  square  centimeter  of  surface?  Ans.  1,033.6  g. 

8.  A  certain  room  is  10  m.  long,  8  m.  wide,  and  4  m.  high,     (a) 
What  weight  of  air  does  it  contain?     (6)  What  is  the  pressure  upon 
its  floor?     (c)  Upon  its  ceiling?     (d)   Upon  each  end?     (e)  Upon 
each  side?     (/)  What  is  the  total  pressure  upon  the  six  surfaces? 
(g)  Why  is  not  the  room  torn  to  pieces  ? 

9.  An*  empty  toy  balloon  weighs  5  g.     When  filled  with  10  1.  of 
hydrogen,  what  load  can  it  lift  ?    A  liter  of  hydrogen  weighs  0.0896  g. 

Elastic  Force. 

Experiment  83.  —  Tightly  close  the  opening  of  a  toy  balloon,  foot- 
ball, or  other  rubber  bag,  only  partly  filled  with 
air.  Place  it  under  the  receiver  of  an  air-pump, 
as  shown  in  the  accompanying  figure,  and  ex- 
haust the  air  from  the  receiver.  The  flexible 
wall  of  the  bag  will  be  pushed  back  by  the  in- 
numerable impacts  of  the  moving  molecules 
against  the  confining  surface.  The  observed 
phenomenon  is  in  strict  accord  with  the  kinetic 
theory  of  gases,  §  51. 

Experiment  84.  —  For  the  rubber  bag  of  Ex- 
periment 83,  substitute  successively  a  dish  containing  soap-bubbles, 


THE   MECHANICS  OF   GASES.  187 

and  a  bottle  with  its  mouth  opening  under  water  in  a  tumbler.  Ex- 
haust the  air  as  before,  and  notice  the  effect  of  the  molecular  impacts 
on  the  liquid  walls  of  the  confined  air. 

Experiment  85.  —  Half  fill  a  small  bottle  with  water,  and  close  the 
neck  with  a  cork  through  which  a  small  tube  passes.  The  lower  end 
of  this  tube  should  dip  into  the  liquid ;  the  upper  end  should 
be  drawn  out  to  a  jet.  Apply  the  lips  to  the  upper  end  of 
the  tube,  and  force  air  into  the  bottle. 

Experiment  86.  —  Place  the  bottle,  arranged  as  above 
described,  under  the  receiver  of  an  air-pump,  and  exhaust 
the  air  from  the  receiver.  Water  will  be  driven  in  a  jet 
from  the  tube. 

Experiment  87.  —  Apparatus   dealers  supply   "  bursting 

squares "  made  of  thin  glass,  and  sealed  F~ 
under  the  ordinary  atmospheric  pressure. 
Place  one  of  these  "  squares  "  upon  the  plate  of  the  air- 
pump,  cover  it  with  wire  netting  as  a  protection  against 
accident,  and  over  all  place  a  bell-glass.  Exhaust  the 
air  from  the  bell-glass,  and  the  elastic  force  of  the  air 
confined  in  the  square  will  burst  the  thin  glass  walls 

FIG.  136.       outward. 

168.  Elastic  Force  of  Gases.  —  When  a  glass  vessel  (see 
Fig.  126)  is  open,  the  atmospheric  pressure  on  the  outer 
surface  is  exactly  balanced  by  the  pressure  on  the  inner 
surface.  Closing  the  stopcock  will  not  destroy  the 
equality  of  pressures ;  the  elastic  force  of  the  confined  gas 
will  just  equal  the  pressure  of  the  surrounding  atmosphere. 
If  the  stopcock  is  closed  when  the  gas  is  under  a  pressure 
of  two  atmospheres,  the  equality  will  still  continue,  each 
being  about  thirty  pounds  per  square  inch.  In  neither 
case  will  the  vessel  be  subjected  to  any  stress  by  the  gas 
within  or  without.  The  elastic  force  of  a  gas  supports  and 
equals  the  pressure  exerted  upon  it. 


188 


SCHOOL  PHYSICS. 


Relation  of  Volume  to  Pressure. 

Experiment  88.  —  Provide  a  stout  glass  tube  more  than  a  meter 
long,  bent  as  shown  in  Fig.  137,  the  short  arm  being  closed.  Pour  a 
small  quantity  of  mercury  into  the  tube  so  that  its  surfaces  in  the  two 
tubes  are  in  the  same  horizontal  line.  By  holding  "the  tube  nearly 
level,  bubbles  of  air  may  be  passed  into  the  short  arm  or  from  it  until 

the  desired  result  is 
secured.  The  air  in 
the  short  arm  will 
then  be  under  a  pres- 
sure of  one  atmos- 
phere. Fasten  the 
tube  to  an  upright 
support,  and  place  a 
scale  graduated  to 
millimeters  by  each 
arm,  the  zero  of  each 
scale  being  just  at  the 
mercury  levels.  Pour 
mercury  into  the  long 
arm  of  the  tube,  thus 
increasing  the  pres- 
sure on  the  air  con- 
fined in  the  short 
arm.  When  the  ver- 
tical distance  between 
the  levels  of  the  mer- 
cury in  the  two  arms 
is  one  fourth  the 
height  of  the  baro- 
metric column  at  the 
time  and  place  of  the 
experiment,  the  pres- 
sure upon  the  confined 
air  will  be  f  atmos- 
pheres, i.e.,  a  pressure  of  about  95  cm.  of  mercury ;  the  elastic  force 
of  the  confined  air  just  supports  this  pressure,  and  must,  therefore, 
be  £  atmospheres ;  the  volume  of  the  confined  air  is  f  what  it  was 
under  a  pressure  of  one  atmosphere.  Tf  more  mercury  is  added 


FIG.  137. 


THE    MECHANICS   OF   GASES. 


189 


until  the  vertical  distance  between  the  two  mercurial  surfaces  is 
half  the  height  of  the  barometric  column,  the  pressure  and  the  elastic 
force  will  be  f  atmospheres,  or  about  114  cm.  of  mercury;  the  volume 
of  the  confined  air  will  be  f  what  it  was  under  a  pressure  of  one 
atmosphere.  When  mercury  has  been  poured  into  the  long  arm  until 
the  vertical  distance,  CA,  is  equal  to  the  height  of  the  barometric 
column,  the  pressure  will  be  two  atmospheres,  or  about  152  cm.  of 
mercury,  and  the  volume  of  the  confined  air  will  be  half  what  it  was 
under  a  pressure  of  one  atmosphere. 

Experiment  89.  —  Nearly  fin  the  barometer  tube  used  in  Experi- 
ment 81,  or  a  similar  tube  more  than  half  as  long  and  graduated  to 
cubic  centimeters,  with  mercury,  and  invert  it 
over  a  mercury-bath  as  shown  in  Fig.  138. 
Lower  the  tube  into  the  tank  until  the  mercury 
within  the  tube  and  without  it  is  at  the  same 
level.  The  confined  air  is  under  the  same  pres- 
sure as  the  external  air;  e.g.,  76  cm.  of  mer- 
cury. Note  the  volume  of  the  confined  air. 
Raise  the  tube  until  this  volume  of  the  confined 
air  is  doubled,  and  measure  the  height  of  the 
mercury  column  in  the  tube.  It  will  be  found 
that  the  confined  air  is  under  a  pressure  half 
that  of  the  external  air;  e.g.,  38  cm.  of  mer- 
cury. 

Addenda.  —  Suppose  the  volume  of  gas  con- 
fined in  each  of  the  last  two  experiments  meas- 
ured 5  cm.  under  a  pressure  of  one  atmosphere. 
Arrange  the  data  just  obtained  in  the  following 
form,  and  complete  the  table  :  — 


Pressures. 

76 

95 
114 
152 

38 


Volumes. 
5 
4 


10 


Products. 
380 


FIG.  138. 


169.   Boyle's   Law.  —  When   the    temperature   remains 
constant,  the  volume  of  a  gas  varies  inversely  as  the  pres- 


190  '   SCHOOL  PHYSICS. 

sure  upon  it;  i.e.,  the  product  of  a  given  volume  of  gas 
by  its  pressure  is  constant. 

Vcc  — ,  or  V  x  P  =  a  constant  quantity. 

(a)  Later  experiments  have  shown  that  Boyle's  law  is  only 
approximately  true,  and  that  all  gases  deviate  from  it  as  they  near 
the  point  of  liquefaction.  This  law  is  often  called  Mariotte's. 

CLASSROOM  EXERCISES. 

1.  Under  ordinary  conditions,  a  certain  quantity  of  air  measures 
one  liter.     Under  what  conditions  can  it  be  made  to  occupy  (a)  500 
cu.  cm.?     (b)  2,000  cu.  cm.? 

2.  Under   what  circumstances  would  1  cubic  foot  of  air,  at  the 
freezing  temperature,  weigh  about  2£  ounces? 

3.  Into  what  space  must  we  compress  (a)  a  liter  of  air  to  double  its 
elastic  force?     (6)  Two  liters  of  hydrogen ? 

4.  A  barometer  standing  at  30  inches  is  placed  in  a  closed  vessel. 
How  much  of  the  air  in  the  vessel  must  be  removed  that  the  mercury 
may  fall  to  15  inches? 

5.  A  vertical  tube,  closed  at  the  lower  end,  has  at  its  upper  end  a 
frictionless  piston  that  has  an  area  of  1  square  inch.     The  weight  of 
this  piston  is  5  pounds,  and  it  confines  24  cubic  inches  of  dry  steam, 
(a)  What  is  the  elastic  force  of  the  confined  steam  ?     (6)    If  the 
piston  is  loaded  with  a  weight  of   10  pounds,  what  will  be  the 
volume  of  the  confined  steam? 

6.  Mercury  stands  at  the  same  level  in  both  arms  of  a  tube  like 
that  shown  in  Fig.  137.     The  barometer  rises,  and  thereupon  is  noticed 
a  difference  in  the  heights  of  the  two  mercury  columns  in  the  J-tube. 
In  which  arm  does  the  mercury  stand  the  higher  ?    Why  ? 

Siphon. 

Experiment  90.  —  Place  a  pail  of  clean  water  on  the  table,  and  an 
empty  water  pail  on  the  floor.  Place  one  end  of  a  piece  of  thick- 
walled  rubber  tubing,  about  a  yard  long,  in  the  water.  Hold  the 
other  end  of  the  tubing  below  the  level  of  the  table-top,  and  fill  the 
tube  with  water  by  suction.  Notice  the  transfer  of  water  from  one 
pail  to  the  other.  Be  careful  that  the  flexible  walls  of  the  tubing  do 


THE    MECHANICS   OF   GASES.  191 

not  close  upon  each  other  at  the  edge  of  the  upper  pail,  and  thus  cut 
off  the  flow. 

Experiment  91.  —  Change  the  positions  of  the  pails,  placing  the 
one  containing  water  on  the  table.  Gradually  lower  the  rubber  tub- 
ing into  the  water,  allowing  air  to  escape  from  the  upper  end  as  water 
enters  at  the  lower  end.  When  the  tube  is  filled  with  water,  pinch  one 
end  of  it  tightly,  and  carry  it  below  the  level  of  the  table-top.  Raise 
and  lower  this  end  of  the  tubing  to  see  if  the  distance  of  the  opening 
below  the  edge  of  the  upper  pail  has  anything  to  do  with  the  rate  of 
flow. 

Experiment  92.  —  Using  a  bent  glass  tube  of  small  internal  diame- 
ter and  two  tumblers  or  bottles,  arrange  apparatus  to  transfer  water 
from  a  higher  to  a  lower  level,  essentially  as  in  Experiment  91.  Put 
the  apparatus  in  operation  on  the  plate  of  the  air-pump,  cover  it  with 
a  bell-glass,  and  quickly  exhaust  the  air.  The  flow  of  liquid  ceases, 
but  begins  anew  when  air  is  again  admitted. 

170.  The  Siphon  is  essentially  a  tube  with  unequal  arms, 
used  to  carry  liquids  from  one  level,  over  an  elevation,  to 
a  lower  level   by  means   of  atmospheric  pressure.      It  is 
generally  set  in  action  by  filling  it  with  the  liquid,  closing 
its  ends,  placing  the  end  of  the  shorter  arm  in  the  liquid 
to  be  moved,  bringing  the  end  of  the  longer  arm  to  a 
lower  level,  and  then  opening  the  ends.     The  flow  will 
continue  until  the  liquids  stand  at  the  same  level,  or  until 
air  enters  the  tube  at  the  end  of  the  shorter  arm. 

171.  Explanation  of  the  Siphon.  —  The  vertical  distance 
from  the  level  of  the  upper  liquid  to  the  highest  point  of 
the  tube  (ab)  is  the  length  of  one  arm  (see  Fig.  189) ; 
the  vertical  distance  from  the  highest  point  of  the  tube 
to  the  lower  end  of  the  tube,  or  to  the  level  of  the  liquid 
into  which  it  dips  (cd),  is  the  length  of  the  other  arm. 
The  second  of  these  must  exceed  the  first. 

Consider  the  horizontal  layer  of  molecules  in  the  tube 


192 


SCHOOL   PHYSICS. 


d; 

J 


at  the  levels,  a  and  d.  The  atmospheric  pressures,  whether 
direct  or  transmitted  by  the  liquids  in  accordance  with 
Pascal's  law,  will  be  upward  and  equal ;  represent  them 
by  p.  The  weight  of  the  water  in  the  short  arm  produces 
a  downward  pressure  at  a;  represent  this  by  w.  The 

resultant  of  these  forces 
acting  at  a  is  p  —w. 
Similarly,  the  weight  of 
the  water  in  the  long 
arm  produces  a  down- 
ward pressure  at 
represent  this  by  w' 
The  resultant  of  these 
forces  acting  at  d  is 
p  —  w'.  These  two  re- 
sultants act  against 
each  other,  p—w  being 
the  greater.  The  result- 
ant of  these  resultants 
is  their  difference  ;  (p  —  w)  —  (p  —  w')=wf—w.  Thus  we 
see  that  the  liquid  is  pushed  through  the  tube  by  a  net 
force  equal  to  the  weight  of  a  liquid  column  whose  height 
is  the  difference  between  the  two  arms  of  the  siphon. 

(a)  Suppose  the  siphon  to  have  a  cross-section  of  1  sq.  cm. ;  that 
db  =  10  cm. ;  that  cd  =  22  cm.  Then  the  upward  pressure  at  a  and  at  d 
will  be  1,033  g. ;  the  downward  pressure  at  a  will  be  10  g. ;  the  down- 
ward pressure  at  d  will  be  22  g.  Then  p  —  w  =  1,023  g. ;  p  —  w'  = 
1,011  g.  The  resultant  of  these  two  upward  and  antagonistic  pres- 
sures (w'  —  w)  is  a  force  of  12  g.  tending  to  push  the  water  from 
a  to  d. 

(6)  If  the  downward  pressure  at  a  is  as  great  as  the  atmospheric 
pressure,  the  liquid  will  not  flow.  Hence,  the  elevation  over  which 
water  is  to  be  siphoned  must  be  less  than  34  feet. 


FIG.  139. 


THE   MECHANICS   OF   GASES. 


193 


Pumps. 

Experiment  93.  —  Every  one  knows  that  a  liquid  may  be  sucked  up 
through  a  straw  or  other  tube.  Modify  the  familiar  experiment  by 
passing  a  glass  tube  snugly  through  the  cork  of  a  bottle.  Fill  the 
bottle  with  water,  and  close  it  with  the  perforated  cork.  Be  sure  that 
no  air  is  left  in  the  bottle.  The  tube  should  dip  an  inch  or  so  into 
the  water.  Try  to  suck  water  from  the  bottle. 

172.  The  Lift  Pump  or  suction-pump  consists  of  a 
cylinder  or  barrel,  piston,  two  valves,  and  a  suction-pipe, 
the  lower  end  of  which  dips  below 
the  surface  of  the  liquid  to  be  raised. 
The  piston  works  practically  air-tight 
in  the  cylinder,  and  has  an  outlet- valve 
that  opens  upward.  The  inlet-valve  is 
at  the  upper  end  of  the  suction-pipe, 
and  also  opens  upward.  When  the 
piston  is  drawn  upward,  its  valve 
is  closed  by  the  pressure  of  the  air 
above,  and  a  partial  vacuum  is  formed 
in  the  cylinder  below.  The  elastic 
force  of  the  air  in  the  cylinder  being 
thus  reduced,  the  atmospheric  pres- 
sure forces  water  up  the  suction-pipe, 
driving  the  air  above  it  through  the 
lower  valve.  When  the  piston  is  pushed  down,  the  inlet- 
valve  is  closed,  and  the  confined  air  escapes  through  the 
outlet-valve.  As  the  piston  continues  its  work,  the  air  is 
gradually  removed  from  the  cylinder  and  suction-pipe, 
and  the  transmitted  pressure  of  the  atmosphere  pushes 
the  water  up  to  take  its  place  and  to  restore  the  disturbed 

equilibrium. 
13 


FIG.  140. 


194 


SCHOOL  PHYSICS. 


(a)  Theoretically  the  piston  may  be  34  feet  above  the  level  of  the 
water  in  the  well,  but,  owing  to  mechanical  imperfections,  the  prac- 
tical limit  for  a  pump  lifting  water  by  suction  is  about  28  vertical  feet. 
The  height  to  which  water  may  be  lifted  above  the  piston  depends 
only  upon  the  strength  of  the  pump  and  the  power  applied. 


173. 

pump 


The  Force  Pump.  —  The  operation  of  the  force- 
is  similar  to  that  of  the  suction-pump.  The  outlet- 
valve  generally  opens  from  the  cylin- 
der, the  piston  being  made  solid.  When 
the  piston  is  raised,  water  is  forced  into 
the  barrel  by  atmospheric  pressure. 
When  the  piston  is  forced  down,  the 
inlet-valve  is  closed,  the  water  being 
forced  through  the  other  valve  into 
the  discharge-pipe.  When  next  the  pis- 
ton is  raised,  the  outlet-valve  is  closed, 
preventing  the  return  of  the  water 
above  it,  while  atmospheric  pressure 
forces  more  water  from  below  into  the 
barrel. 


FIG.  141. 


(a)  For  the  purpose  of  securing  steadiness 
for  the  stream  as  it  issues  from  the  delivery- 
pipe,  the  water  usually  passes  into  an  air-chamber.  The  elasticity 
of  the  confined  and  compressed  air  largely  takes  up  the  pulsating 
effect  due  to  the  successive  pushes  of  the  piston,  and  forces  the  water 
from  the  nozzle  of  the  delivery-pipe  in  a  continuous  stream.  Fire- 
engines  and  nearly  all  steam-pumps  have  such  attachments. 

174.  The  Air  Pump  is  an  instrument  for  removing  a  gas 
from  a  closed  vessel.  Fig.  142  shows  the  essential  parts 
of  one  of  the  many  forms. 

(a)  The  glass  receiver,  jR,  fits  accurately  upon  the  ground  plate. 
The  edge  of  the  receiver  is  often  greased  to  insure  an  air-tight  joint. 


THE   MECHANICS  OF   GASES. 


195 


From  R,  a  tube,  «,  leads  to  the  cylinder,  C,  in  which  moves  a  piston,  P. 
Two  valves  open  from  the  receiver.  The  outlet-valve,  v',  is  in  the 
piston  ;  the  inlet-valve,  v,  may  be  carried  by  a  rod  that  passes  through 
the  piston.  Of  course  the  piston,  valve,  and  all  sliding  parts  of  the 
pump,  must  work  air-tight.  A  down-stroke  of  the  piston  carries  down 
the  valve-rod,  and  closes  v ;  the  elastic  force  of  the  air  confined  beneath 
P  opens  v',  and  some  of  the  air  escapes  to  the  upper  side  of  the  piston. 
The  next  up-stroke  of  the  piston  closes  v'  and  lifts  the  valve-rod,  and 
thus  opens  v.  The  upward  motion  of  the  valve-rod  is  closely  limited 
by  a  shoulder  near  its  upper  end,  the  piston  sliding  upon  the  rod 
during  the  greater  part  of  its  up-and-down  movements.  The  air  that 


FIG.  142. 

passes  up  through  vf  is  forced  out  through  an  opening  (preferably 
closed  by  a  valve)  at  the  top  of  the  cylinder,  and  the  elastic  force  of 
the  air  in  R  and  t  fills  again  the  lower  part  of  C.  By  the  continued 
working  of  the  piston,  the  mass  and  the  elasticity  of  the  air  in  R  are 
reduced,  a  vacuum  being  approached  more  and  more  closely.  As  only 
a  fractional  part  of  the  residual  air  is  removed  at  each  stroke,  a  per- 
fect vacuum  is  out  of  the  question ;  moreover,  there  is  a  limit  arising 
from  the  unavoidable  imperfections  of  the  apparatus. 

(6)  In  Fig.  142,  F  is  a  glass  vessel  communicating  with  the  re- 
ceiver. It  contains  a  siphon-barometer  or  mercurial  gauge  to  indi- 
cate the  degree  of  rarefaction  obtained.  A  stopcock  at  S,  when 
turned  one  way,  cuts  off  communication  between  C  and  R,  thus 


196 


SCHOOL   PHYSICS. 


FIG. 143. 


reducing  the  risk  that  air  will  reenter  the  receiver ;  when  turned  the 
other  way,  it  readmits  air  to  R. 

175.    The  Condensing  Pump  is  an  instrument  for  com- 
pressing a  gas  into  a  closed  vessel,  as   in   pumping   air 
into  a  pneumatic  tire  of  a  bicycle,  or  oxygen  or  hydro- 
gen  into  the  cylinders  commonly  used   for   stereopticon 
purposes,    or  charging   water  with   carbon 
dioxide  for  sale  as  "soda  water." 

(a)  It  differs  from  the  air-pump  chiefly  in  the  facts 
that  the  valves  are  made  strong  enough  to  endure 
high  pressures,  and  that  they  open  toward  the  re- 
ceiver. For  some  purposes,  the  piston  is  made  solid, 
and  both  valves  are  placed  at  the  bottom  of  the 
cylinder,  as  shown  in  Fig.  143.  The  stopcock  at  R 
is  closed  while  the  pump  is  in  operation.  By  con- 
necting each  of  the  lateral  tubes  with  a  closed  tank, 
gas  may  be  transferred  from  one  to  the  other. 

CLASSROOM  EXERCISES. 

1.  How  high  can  water  be  raised  by  a  perfect  lift-pump,  when 
the  barometer  stands  at  30  inches  ?     The  density  of  mercury  is  13.6. 

2.  If  a  lift-pump  can  just  raise  water  28  feet,  how  high  can  it 
raise  alcohol  having  a  density  of  0.8  ? 

3.  Water  is  to  be  taken  over  a  ridge  12.5  m.  higher  than  the  surface 
of  the  water,     (a)  Can  it  be  done  with  a  siphon  ? 

Why?     (6)  With   a  lift-pump?    Why?     (c)  With  a 
force-pump  ?     Why  ? 

4.  Will  a  given  siphon  carry  water  over  a  given 
elevation  more  rapidly  at  the  top,  or  at  the  bottom,  of 
a  mountain?    Why? 

5.  If  water  rises  34  feet  in  an  exhausted  tube,  how 
high  will  sulphuric  acid  (density,  1.8)  rise  under  the 
same  circumstances  ? 

6.  The   "sucker"   consists  of  a   circular  piece  of 
thick  leather  with  a  string  attached  to  its  middle. 
Being  soaked  thoroughly  in  water,  it  is  firmly  pressed 

upon  a  flat  stone  to  drive  out  all  air  from  between  the  leather  and 


FIG. 


THE   MECHANICS  OF   GASES. 


197 


the  stone.  Unless  the  stone  is  too  heavy,  it  may  be  lifted  by  the 
string.  Is  the  stone  really  pulled  up,  or  pushed  up  ?  Explain  your 
answer. 

7.  If  the  capacity  of  the  cylinder  of  an  air-pump  is  £  that  of  the 
receiver,  (a)  what  part  of  the  air  will  remain  in  the  receiver  at  the 
end  of  the  fourth  stroke  of  the  piston?     (6)  How  will  its  elastic  force 
compare  with  that  of  the  external  air  ? 

8.  How  high  can  a  liquid  with  a  density  of  1.35  be  raised  by  a 
perfect    lift-pump    -when    the    barometer 

stands  at  29.5  inches? 

9.  Over  how  high  a  ridge  can  water  be 
continuously  carried  in  a  siphon,  the  mini- 
mum standing  of  the  barometer  being  69 
cm.  ? 

10.  What  is  the  greatest  pull  that  can 
be    resisted   by   Magdeburg    hemispheres 
(a)  4  inches  in  diameter?     (&)  8  cm.  in 
diameter  ? 

11.  How  can  you  arrange  a  single  lift- 
pump  to  raise  water  from  the  bottom  of 
a  well  50  feet  deep  ? 

12.  Construct  the  apparatus   shown  in 
Fig.  145,  filling  each  of  the  three  bottles 
half  full  of  water.     Be  sure  that  all  joints 
made  by  the  corks  of  the  three  bottles  are 


FIG.  145. 


air-tight.     Blow  into  the  tube,  /,  until  a  jet  is  formed  at  n. 
plain  the  continued  action  of  the  apparatus. 


EX- 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Small  test-tube;  pen-filler;  sulphuric 
ether ;  pinchcock ;  lead  counterpoise. 

1.  Partly  fill  two  bottles  with  water.  Con- 
nect them  by  a  bent  tube  that  fits  closely  into 
the  mouth  of  one,  and  loosely  into  the  mouth  of 
the  other.  Place  the  bottle  under  the  receiver 
and  exhaust  the  air.  Note  and  record  what 
takes  place.  Admit  air  to  the  receiver.  Note 
and  record  what  takes  place.  Write  an  explana- 
tion of  the  phenomena. 


FIG.  146. 


198  SCHOOL  PHYSICS. 

2.  Fill  a  test-tube  with  water  and  invert  it  in  a  tumbler  of  water. 
With  a  pen-filler,  introduce  a  few  drops  of  sulphuric  ether,  a  very 
volatile  and  extremely  inflammable  liquid,  into  the  test-tube.     The 
ether  will  rise  to  the  top  of  the  tube.     Place  the  tumbler  and  the  test- 
tube  under  the  receiver  and  exhaust  the  air.     The  water  in  the  test- 
tube  falls.     Readmit  air  to  the  receiver,  and  note  the  contents  of  the 
test-tube.     Record  your  conclusions  concerning  the  effect  of  pressure 
upon  the  molecular  condition  of  sulphuric  ether. 

3.  With  a  short  piece  of  rubber  tubing,  connect  the  short  arms  of 
two  |_-shaped  glass  tubes,  and  set  up  the  apparatus  as  a  siphon.    While 
the  water  is  flowing,  perforate  the  rubber  wall  between  the  glass  tubes. 
Note  and  explain  the  effect. 

4.  With  apparatus  like  that  used  in  Experiments  88  and  89,  and 
noting  the   reading  of  the  mercurial  barometer  at  the  time,  verify 
Boyle's  law  between  the  limits  of  half  an  atmosphere  and  two  atmos- 
pheres, by  showing  the   constancy  of  the   product   of  volume  into 
pressure. 

5.  Fill  the    U'tube  used  in   Experiment   63   with   mercury  to  a 
depth  of  about  30  cm.,  and  attach  a  rubber  tube  about  40  or  50  cm. 
long  firmly  to  one  end  of  the  tube.    Force  air  steadily  from  the  lungs 
through  the  rubber  tube ;  pinch  the  tube  tightly ;  rest ;  increase  the 
pressure  on  the  mercury  if  you  can  without  injury  or  pain  ;  close  the 
rubber  tube  with  a  pinchcock;  and  compute  your  maximum  "lung 
power  "  in  pounds  per  square  inch. 

6.  With  the  same  apparatus,  suck  air  from  the  tube,  and  compute 
your  maximum  "force  of  suction "  in  pounds  per  square  inch.    Explain 
the  use  of  quotation  marks  in  the  last  sentence. 

7.  With  the  same  apparatus,  measure  the  pressure  under  which 
illuminating  gas  is  delivered  at  the  laboratory.     Will  you  get  more 
accurate  results  by  using  mercury,  or  water  ? 

8.  What  objection  is  there  to  using  the  same  apparatus  for  measur- 
ing the  pressure  under  which  water  is  supplied  at  the  laboratory? 
Devise  some  means  for  that  problem,  and  solve  it. 

9.  Repeat  Experiment  73.     Determine  the  capacity  of  the  vessel 
used.     Compare  the  reading  of  the  pressure-gauge  of  the  air-pump 
with  that  of  the  barometer  at  the  time  of  the  experiment,  and  deter- 
mine what  part  of  the  air  in  the  vessel  was  removed.      Determine 
the  density  of  air  under  the  thermometric  and  barometric  conditions 
of  the  experiment.     If  you  have  no  vessel  like  that  mentioned  in 
Experiment  73,  use  a  2-liter   bottle,  connecting  its   rubber   stopper 


THE   MECHANICS   OF   GASES.  199 

with  the  pump  by  a  thick-walled  rubber  tube.  After  exhaustion, 
close  the  tube  with  a  pinchcock.  Make  all  connections  air-tight, 
using  glycerin  for  that  purpose.  Be  sure  not  to  omit  any  of  the 
apparatus  from  one  weighing,  that  is  included  in  the  other. 

10.  Fill  with  mercury  the  tube  used  in  Experiment  81,  and  by 
direct  weighing  and  measurement,  determine  the  weight  of  the  mer- 
cury per  centimeter  of  the  length  of  the  tube.     Measure  the  length  of 
the  barometric  column  in  the  same  tube  and  compute  the  weight 
of  the  mercury  supported  by  atmospheric  pressure. 

11.  Make  a  siphon  with  parallel  arms,  each  about  50  cm.  long,  by 
bending  a  piece  of  glass  tubing  twice  at  right  angles.     Place  one 
branch  of  the  tube  in  a  large  vessel  of  water  at  least  40  cm.  deep,  and 
support  the  siphon  so  that  its  short  arm  shall  be  10  cm.  long.     (See 
§  170.)    Start  the  siphon  by  suction,  and  measure  with  a  graduate  the 
water  that  flows  in  two  minutes.     Determine  the  difference  between 
the  lengths  of  the  two  arms.     Raise  the  siphon  until  its  short  arm  is 
15  cm.  long.     Set  the  siphon  in  action.     Measure  the  water  that  flows 
in  two  minutes,  and  determine  the  difference  between  the  lengths 
of  the  two  arms,  as  before.     As  this  difference  decreases,  does  the 
amount  of  water    delivered    also    decrease?      Continue    the    work, 
successively  testing  with  short  arm  lengths  of  20,  25,  30,  40,  and 
45  cm.     Tabulate  your  results.      What  is  the  relation  between  rate 
of  flow  and  the  difference  in  the  lengths  of  the  two  arms  of  the 
siphon  ? 

12.  Using  the  differences  in  lengths  of  the  arms  as  ordinates,  and 
the  rate  of  flow  as  abscissas,  map  the  line  that  represents  this  relation. 
From  this  line,  measure  the  abscissa  of  the  point  that  has  an  ordinate 
corresponding  to  a  length  of  35  cm.  for  the  short  arm  of  the  siphon, 
and  determine  the  rate  of  flow  that  it  represents.     Set  the  siphon  used 
in  Exercise  11  so  that  its  short  arm  shall  measure  35  cm.,  and  by 
direct  experiment  test  the  accuracy  of  the  result  computed  from  the 
curve. 

13.  With  the  apparatus  used  in  Experiment  88,  measure  the  com- 
pression of  the  air  confined  under  different  pressures  until  the  excess 
of  mercury  in  the  long  arm  is  about  equal  to  the  barometric  column. 
Avoid  touching  the  short  arm,  or  in  any  way  changing  the  tempera- 
ture of  the  confined  air.     From  the  data  thus  obtained,  map  upon 
cross-section  paper  a  line  representing  the  relation  between  volume 
and  pressure.     Let  each  vertical  division  of  the  paper  represent  a 
pressure  of  2  cm.  of  mercury,  and  each  horizontal  division  a  com- 


200 


SCHOOL   PHYSICS. 


pression  of  0.5  cm. 


Is  the  line  thus  mapped  a  straight  line?  If  so, 
what  does  that  show?  If  the  line  is 
curved,  what  does  the  .varying  down- 
ward slope  indicate  ?  From  the  line 
as  drawn,  do  you  conclude  that  equal 
increments  of  pressure  produce  equal 
compressions,  or  otherwise? 

14.  Using  a  lead  ball  as  shown  in 
Fig.  147,  counterpoise  the  globe  of  Ex- 
periment 73,  "filled  with  air  and  with 
stopcock  closed.  Cover  the  apparatus 
with  a  bell-glass  and  exhaust  the  air. 
The  globe  seems  to  be  heavier  than 
the  ball  which  previously  balanced 
it.  Record  a  description  and  explana- 
tion of  what  you  do  and  of  what  fol- 
lowed. 


FIG.  147. 


CHAPTER   III. 

ACOUSTICS:    MASS  PHYSICS. 
I.    THE   NATURE   OF   SOUND,   ETC. 

176.  Sound  is  the  mode  of  motion  that  is  capable  of  affect- 
ing the  auditory  nerve. 

(a)  We  have  to  deal  with  sound  only  as  a  physical  phenomenon ; 
not  as  a  physiological  or  psychological  process. 

Cause  of  Sound. 

Experiment  94.  —  Suspend  a  small  pith-ball  so  that  it  shall  rest 
lightly  against  the  edge  of  a  bell  or  bell-jar.  Strike  the  bell  so  that 
it  will  give  forth  a  sound.  Such  a  bell  or  a  tuning-fork  may  be 
sounded  by  tapping  it  with  a  hammer  made  by  slipping  a  piece  of 
rubber  tubing  over  a  stout  iron  wire,  or  by  thrusting  the  handle  of  a 
cheap  tapering  pen-holder  into  the  hole  at  the  center  of  a  circular 
eraser.  A  better  way,  however,  is  to  make  it  vibrate  by  drawing  a 
resined  violin-bow  across  the  edge  or  end.  Xotice  that  the  ball  acts 
as  if  the  edge  of  the  bell  was  in  vibration.  Touch  the  edge  of  the 
sounding  bell  lightly  with  the  finger-nail. 

Experiment  95.  —  Sound  a  tuning-fork  and  just  touch  a  water 
surface  with  one  of  its  prongs.  Notice  the  spray. 

Experiment  96.  —  The  chimneys  of  student-lamps  often  break  at 

the  contracted  part  near  the  

bottom.  Close  such  a  broken 
chimney  at  the  broken  end 
with  cork  or  wax.  At  the 
toy  store,  buy  a  wooden  whis- 
tle like  that  shown  in  the 

rIG.  14o. 

upper  part  of  Fig.  148,  and 

cut  it  off  at  the  point  indicated  by  the  dotted  line  between  the  first 

201 


202 


SCHOOL   PHYSICS. 


and  second  finger-holes.  Fit  the  end  of  the  whistle  into  the  opening 
of  a  cork  that  will  tightly  close  the  open  end  of  the  broken  chimney. 
Inside  the  tube,  place  a  small  quantity  of  precipitated  silica,  a  very 
light  powder  that  you  can  buy  from  a  dealer  in  chemical  supplies,  or 
a  like  quantity  of  the  dry  dust  obtained  by  filing  a  cork.  Close  the 
tube  with  the  cork  and  whistle,  hold  the  tube  horizontal  and  shake 
it  endwise  so  as  to  distribute  the  powder  evenly,  and  then  blow  the 

whistle.  The  powder  is  agitated  in 
a  peculiar  manner,  rising  in  thin  ver- 
tical plates,  and  coming  to  rest  in 
little  piles  transverse  to  the  axis  of 
the  tube.  Was  the  motion  of  the  air 
in  the  tube  one  of  vibration,  or  one 
of  translation? 

Experiment   97. —  Grasp   one  end 
of  a  straight  spring  made  of  hickory 
or  steel  in  one  end  of  a  vise,  as  shown 
in  Fig.  149.     Pluck  the  free  end  of 
the  spring  so  as  to  produce  a  vibra- 
tory motion.     If  the  spring  is  long 
enough,  the  vibrations  may  be  seen. 
Lower    the    spring    in    the   vise  to 
shorten  the  vibrating  part  of  the  rod, 
and  pluck  it  again.     The  vibrations 
are    reduced   in  amplitude,  and  in- 
creased in  rapidity.     Continued  shortening  of  the  spring  will  render 
the  vibrations  invisible  and  audible ;  they  are  lost  to  the  eye,  but  re- 
vealed to  the  ear. 

177.  Cause  of  Sound.  —  From  these  experiments,  it  is 
reasonable  to  conclude  that  sound  is  caused  by  the  rapid 
vibrations  of  a  material  body.  In  fact,  all  sounds  may  be 
traced  to  such  vibrations.  Bodies  that  emit  sounds  are 
called  sonorous. 

(a)  A  glass  plate  that  has  been  blackened  by  holding  it  over  a 
petroleum  or  a  camphor  flame  maybe  arranged  so  as  to  slide  easily  in 
the  grooved  frame,  F.  A  triangular  piece  of  tinsel  or  a  short  piece 


FIG.  149. 


THE   NATURE    OF   SOUND,    ETC. 


203 


of  the  hairspring  of  a  watch  attached  by  wax  to  the  end  of  one  of 
the  prongs  of  the  fork  will  make  a  good  style  for  our  purpose.  When 
the  fork  is  made  to  vibrate,  the  style  placed  against  the  smoked  plate, 


150. 


and  the  plate  drawn  along  rapidly  in  the  grooves,  the  undulating  line 
traced  on  the  glass  represents  the  vibratory  movement  of  the  prong. 


Wind  or  Wave? 

Experiment  98.  —  Provide  a  tube  four  or  five  yards  long,  and  about 
four  inches  in  diameter.  A  few  lengths  of  .common  spout  from  the 
tinner's  will  answer.  Furnish  it  with  a  funnel-shaped  piece,  having 
an  opening  about  an  inch  in  diameter.  Place  the  tube  on  a  table  with 
a  candle  flame  opposite  the  opening  at  B.  With  a  book,  strike  a 


FIG.  151. 

sharp  blow  upon  the  table  opposite  the  opening  at  A.  The  flame  will 
be  agitated  and  perhaps  blown  out.  Something  went  from  A  to  B. 
Did  it  go  through  the  tube  ? 

Experiment  99.  —  Close  the  opening  at  A  and  repeat  the  experi- 
ment; the  flame  is  not  put  out.  Remove  the  tube  and  repeat  the 
blow;  the  flame  is  not  put  out. 

Experiment  100.  —  Replace  the  tin  tube  by  a  rubber  tube  of  the  same 
length  and  with  an  internal  diameter  of  about  10  or  15  mm.  Insert 
the  neck  of  a  funnel  at  the  end  of  the  tube  at  A.  Get  a  few  inches 
of  glass  tubing  that  will  fit  snugly  into  the  rubber  tubing.  Heat  the 


204 


SCHOOL   PHYSICS. 


middle  of  the  glass  in  a  flame  until  it  softens.  Slowly  draw  the  ends 
asunder  until  the  softened  part  is  reduced  to  a  diameter  of  about 
2mm.  Break  the  tube  at  this  narrow  neck  and  push  the  large  end  of 
one  piece  into  the  rubber  tube  at  B.  Place  a  small  flame  opposite  the 
small  opening  of  the  glass  tube.  Strike  a  blow  in  front  of  the  funnel 
at  A  and  notice  that  a  puff  or  pulse  of  air  blows  the  flame.  Make  a 
loose  loop  in  the  rubber  tube  and  repeat  the  experiment.  Clap  the 
hands  at  A  and  notice  the  series  of  puffs  at  R.  While  an  assistant  is 
clapping  his  hands  at  A,  pinch  the  rubber  tube.  Notice  that  the  puffs 
at  B  cease  while  the  tube  is  thus  pinched,  and  reappear  as  soon  as  the 
tube  is  released.  The  tube  is  necessary.  Whatever  agitated  the 
candle  flame  did  go  through  the  tube.  Was  this  something  a  wind, 
or  a  wave  ? 

Experiment  101.  —  Replace  the  tin  tube.  Dissolve  as  much  potas- 
sium nitrate  (saltpeter)  as  you  can  in  half  a  cupful  of  hot  water. 
Soak  a  piece  of  blotting-paper  in  this  liquid  and  dry  it.  This  "touch- 
paper  "  burns  with  much  smoke  but  no  flame.  Burn  the  paper  in  the 
tube  near  A,  filling  that  end  of  the  tube  with  smoke.  Repeat  Experi- 
ment 98.  No  smoke  issues  at  B ;  it  ivas  not  a  wind  that  passed  through 
the  tube. 

178.  Propagation  of  Sound.  — Sound  is  ordinarily  propa- 
gated through  the  air.  Tracing  the  sound  from  its  source 
to  the  ear  of  the  hearer,  we  may  say  that  the  first  layer  of 
air  is  struck  by  the  vibrating  body.  The  particles  of  this 

layer  give  their  mo- 
tion to  the  particles 
of  the  next  layer, 
and  so  on  until  the 
particles  of  the  last 
layer  strike  upon 
the  drum  of  the 


FIG.  152. 


ear. 


(a)    This  idea  is  beautifully  illustrated  by  Professor  Tyndall.     He 
imagines  five  boys  placed  in  a  row,  as  shown  in  Fig.  152.     "I  sud- 


THE   NATURE   OF   SOUND,    ETC.  205 

denly  push  A  ;  A  pushes  B  and  regains  his  upright  position ;  B 
pushes  C ;  C  pushes  D ;  D  pushes  E ;  each  boy,  after  the  transmission 
of  the  push,  becoming  himself  erect.  E,  having  nobody  in  front,  is 
thrown  forward.  Had  he  been  standing  on  the  edge  of  a  precipice, 
he  would  have  fallen  over ;  had  he  stood  in  contact  with  a  window,  he 
would  have  broken  the  glass ;  had  he  been  close  to  a  drumhead,  he 
would  have  shaken  the  drum.  We  could  thus  transmit  a  push 
through  a  row  of  a  hundred  boys,  each  particular  boy,  however,  only 
swaying  to  and  fro.  Thus  also  we  send  sound  through  the  air,  and 
shake  the  drum  of  a  distant  ear,  while  each  particular  particle  of  the 
air  concerned  in  the  transmission  of  the  pulse  makes  only  a  small 
oscillation." 

The  Medium  of  Sound. 

Experiment  102.  —  Place  a  small  music  box  or  alarm  clock  on  a 
thick  layer  of  felt,  cotton  wool,  or  other  inelastic  material  on  the 
plate  of  the  air-pump,  and  cover  it  with  a  bell-glass.  Exhaust  the 
air  and  notice  that  while  the  motion  of  the  mechanism  is  plainly 
visible,  the  sound  is  scarcely  audible. 

Experiment  103.  —  In  a  large  glass  globe  provided  with  a  stopcock, 
suspend  a  small  bell  by  a  thread.  Pump  the 
air  from  the  globe ;  shake  the  globe,  and  notice 
that  the  sound  of  the  bell  is  very  faint.  Re- 
admit the  air;  shake  the  globe,  and  notice  that 
the  sound  of  the  bell  is  heard  distinctly.  A 
large,  wide-mouthed  bottle,  with  a  perforated 
rubber  stopper,  rubber  tubing,  and  pinchcock, 
may  be  substituted  for  the  globe  and  stopcock. 
See  Experiment  73. 

Experiment  104.  —  Fill  a  tumbler  with  water  and  place  it  on  an 
empty  crayon  box.  Stick  the  stem  of  a  tuning-fork  into  a  small 
wooden  disk,  sound  the  fork,  and  hold  it  with  the  disk  resting  upon 
the  surface  of  the  water.  The  vibrations  will  be  transmitted  by  the 
water,  and  the  sound  of  the  fork  will  be  heard  as  if  coming  from  the 
box.  Other  liquids  may  be  similarly  tested. 

Experiment  105.  —  Provide  a  wooden  rod  about  half  an  inch  square 
and  five  or  six  feet  long.  Place  one  end  of  this  rod  (preferably  made 
of  light,  dry  pine)  agamst  the  panel  of  a  door;  hold  the  rod  hori- 


206  SCHOOL   PHYSICS. 

zontal,  and  place  the  handle  of  a  vibrating  tuning-fork  against  the 
other  end.  Notice  the  sound  given  out  by  the  panel.  The  common 
"  string  telephone  "  is  a  more  familiar  illustration  of  the  transmission 
of  sound  by  a  solid. 

179.  Sound  Media.  —  Any  elastic  substance  may  be  the 
medium  for  the  transmission  of  sound.     Liquids  and  solids 
are  better   conductors   of   sound   than   gases   are.      The 
scratching  of  a  pin  may  be  heard  through  a  long  wooden 
beam ;  and  the  gentle  tap  of  a  hammer,  through  a  water- 
pipe  a  mile  or  more  in  length.     The  nature  of  the  vibra- 
tions in  sound-media  demands  careful  consideration. 

Vibratory  Motion. 

Experiment  106.  —  Grip  one  end  of  the  meter  stick  in  a  vise,  as 
shown  in  Fig.  149.  Pluck  the  free  end,  and  notice  that  the  vibrating 
end  returns  periodically  to  the  starting  point.  Suspend  a  lead  bullet 
by  a  long  thread,  swing  it  as  a  pendulum,  and  notice  that  the  ball 
returns  periodically  to  the  starting  point.  Swing  the  ball  as  a  conical 
pendulum,  and  notice  that  the  ball,  moving  in  a  circular  path,  returns 
periodically  to  the  starting  point.  Twist  the  torsion al  pendulum 
(Experiment  17),  and  notice  that  the  index  returns  periodically  to  the 
starting  point. 

Experiment  107.  —  Fasten  an  elastic  cord  to  a  ball,  or  buy  a  "  return 
ball "  at  a  toy  shop.  Hold  the  end  of  the  cord  in  one  hand,  and,  with 
the  other  hand,  pull  the  ball  down  and  let  it  go.  The  ball  swings  up 
and  down  in  the  direction  of  the  length  of  the  cord.  Notice  that  the 
speed  of  the  ball  varies  much  as  does  that  of  a  common  pendulum, 
and  that  the  ball  returns  periodically  to  the  starting  point. 

180.  Vibrations.  —  When  the  parts  of  a  body  move  so 
that  each  returns  periodically  to  its  initial  position,  the 
body  is  said  to  be  in  vibration.      The  motion  made  in  the 
interval  between  two  successive  passages  in  the  same  direction 
through  any  position  is  called  a  vibration.     The  vibration 
may  be  transverse,  torsional,  or  longitudinal,  the  classifi- 


THE  NATURE  OF  SOUND,  ETC.          207 

cation  having  reference  to  the  direction  of  the  vibration 
relative  to  the  length  of  the  vibrating  body. 

(a)  A  vibration  is  analogous  to  a  double  or  "  complete  "  oscillation, 
as  defined  in  §  114  (a).  When  the  reciprocating  movement  is  com- 
paratively slow,  as  that  of  a  pendulum,  the  term  "  oscillation "  is 
commonly  used ;  the  term  "  vibration  "  is  generally  confined  to  rapid 
reciprocations  or  revolutions,  as  that  of  a  sonorous  body.  The  three 
kinds  of  vibration  have  the  same  manner  of  moving,  the  changes 
in  velocity  being  the  same  as  take  place  in  the  swings  of  a  pen- 
dulum. 

Pendular  Motion. 

Experiment  108.  —  Let  a  pupil  take  a  ball-and-thread  pendulum  to 
the  further  side  of  the  room.  With  a  slight  circular  motion  of  the 
hand  that  supports  the  end  of  the  thread,  let  him  cause  the  ball  to 
move  in  a  circular  path,  thus  forming  a  conical  pendulum.  When 
the  speed  of  the  ball  has  become  uniform,  count  the  swings  that  the 
ball  makes  around  the  circle  in  30  seconds.  Then  place  your  eye  on 
a  level  with  the  ball  and  observe  it ;  i.e.,  look  at  the  ball  along  a  line 
of  sight  that  is  in  the  plane  of  the  circle. 
The  ball  will  appear  to  move  from  side  to  side 
in  a  straight  line  that  coincides  with  a  diam- 
eter of  the  circle,  and  to  vary  its  velocity  as  a 
common  pendulum  does.  Xext,  swing  the 
same  ball  as  a  common  pendulum,  and  count 
the  vibrations  that  it  makes  in  30  seconds. 
A  conical  pendulum  and  a  common  pendu- 
lum of  the  same  length  have  the  same  period. 
When  the  common  pendulum  is  viewed  from 
beneath,  i.e.,  when  the  line  of  sight  is  in  the 
plane  of  vibration  as  before,  the  bah1  again  appears  to  move  in  a 
straight  line  and  with  a  like  varying  velocity.  This  apparent  motion 
and  its  relation  to  the  real  motion  are  very  interesting  and  instructive. 
Let  the  circle  shown  in  Fig.  154  represent  the  path  described  by  the 
conical  pendulum;  then  will  the  diameter,  A  G,  represent  the  apparent 
rectilinear  path.  Suppose  that  the  ball  goes  around  the  circle  in  two 
seconds.  Divide  the  circumference  into  any  number  of  equal  parts, 
as  12.  The  ball  will  move  over  each  of  these  equal  arcs  in  £  of  a 


208  SCHOOL  PHYSICS. 

second.  To  one  who  is  looking  at  this  motion  in  the  plane  of  the 
paper,  the  ball  appears  to  go  from  A  to  B  while  it  really  goes  from 
A  to  b;  it  appears  to  go  from  B  to  C  while  it  really  goes  from  b  to  c; 
etc.  When  the  ball  is  at  d,  it  is  moving  across  the  line  of  sight,  and, 
therefore,  appears  to  have  its  greatest  velocity,  just  as  a  common 
pendulum  does,  at  the  middle  of  its  arc.  When  it  is  at  A  or  G,  it  is 
moving  in  the  line  of  sight,  and,  therefore,  appears  to  be  at  rest, 
although  it  is  really  moving  with  its  uniform  velocity.  From  a  study 
of  the  figure,  it  will  be  seen  that  the  ball  appears  to  go  from  A  to  G 
and  back  in  the  two  seconds  in  which  it  really  goes  around  the  circle. 
The  unequal  lengths,  AB,  BC,  .  .  .  FG,  give  a  fair  idea  of  the  varying 
speed  of  a  common  pendulum. 

181.  Simple  Harmonic  Motion.  —  If,  while  a  particle 
moves  in  the  circumference  of  a  circle  with  uniform  ve- 
locity, a  point  moves  along  a  fixed  diameter  of  the  circle 
so  as  always  to  be  at  the  foot  of  a  perpendicular  drawn 
from  the  particle  to  the  diameter,  as  described  in  Experi- 
ment 108,  the  motion  of  the  point  along  the  diameter  is 
called  a  simple  harmonic  motion.  The  radius  of  the  circle, 
or  the  distance  from  the  middle  to  the  extremity  of  the 
swing,  is  called  the  amplitude  of  vibration ;  the  time  inter- 
vening between  two  passages  of  the  particle  in  the  same 
direction  through  any  point  is  called  the  period  of  vibra- 
tion. 

Wave  Forms. 

Experiment  109.  —  Drop  a  pebble  into  a  tub  of  water.  Waves  will 
be  seen  moving  on  the  surface  of  the  water  from  the  center  of  dis- 
turbance, and  in  concentric  circles,  toward  the  sides  of  the  tub.  A 
small  cork  floating  on  the  surface  rises  and  falls  with  the  water, 
but  is  not  carried  along  by  the  advancing  waves  of  troughs  and 
crests. 

Experiment  no.  —  Tie  one  end  of  a  soft  cotton  rope  about  20  feet 
long  to  a  fixed  support,  and  hold  the  other  end  in  the  hand.  Move 
the  hand  up  and  down  with  a  quick,  sudden  motion,  so  as  to  set  up  a 


THE  NATURE  OF  SOUND,  ETC.          209 

series  of  waves  in  the  rope,  as  shown  in  Fig.  155,  in  which  each 
curved  line  may  be  considered  an  instantaneous  photograph  of  a  rope 
thus  shaken. 


FIG.  155. 

182.  Waves  of  Crests  and  Troughs.  —  When  a  person 
sees  waves  approaching  the  shore  of  a  lake  or  ocean, 
there  arises  the  idea  of  an  onward  movement  of  great 
masses  of  water.  But  if  the  observer  watches  a  piece 
of  wood  floating  upon  the  water,  he  may  notice  that  it 
merely  rises  and  falls  without  approaching  the  shore. 
Again,  he  may  stand  beside  a  field  of  ripening  grain,  and, 
as  the  breezes  blow,  he  will  see  a  series  of  curved  forms 
or  waves  pass  before  him.  There  is  no  movement  of  mat- 
ter from  one  side  of  the  field  to  the  other ;  the  grain- 
ladened  stalks  merely  bow  and  raise  their  heads.  Most 
persons  are  familiar  with  similar  wave  movements  in 
ropes,  chains,  and  carpets.  Each  material  particle  has  a 
simple  harmonic  motion,  vibratory,  not  progressive.  The 
only  thing  that  has  an  onward  movement  is  the  pulse  or 
ivave,  which  is  only  a  form  or  change  in  the  relative  posi- 
tions of  the  particles  of  the  undulating  substance. 

(a)  By  fixing  a  pencil  at  the  end  of  a  lath  firmly  held  at  the  other 
end,  and  vibrating  in  a  horizontal  plane,  the  pencil  may  be  made  to 
mark  a  nearly  straight  line,  ab,  on  a  sheet  of  paper  or  cardboard.  By 
moving  the  paper  while  the  rod  is  vibrating,  the  pencil  may  be  made 
to  trace  a  sinusoidal  curve  or  wavy  line  like  that  shown  in  Fig.  156. 
The  construction  of  such  a  curve,  and  its  relation  to  the  simple  har- 
monic motion  of  the  pendulum,  will  be  further  illustrated  in  the 
exercises.  The  distance  from  crest  to  crest  (1  to  5),  or  from  trough  to 
14 


210 


SCHOOL   PHYSICS. 


trough  (3  to  7),  or  from  any  point  to  the  next  point  at  which  the 
vibrating  particle  was  in  the  same  stage  of  vibration  or  in  the  same 
phase  (A  to  4,  or  2  to  6,  or  4  to  J3),  is  called  a  wave-length.  Evidently, 


FIG.  156. 

the  disturbance,  i.e.,  the  wave,  advances  just  one  wave-length  in  the 
time  required  for  one  vibration;  this  time  is  called  the  vibration- 
period. 

Experiment  in.  —  Make  a  spiral  spring  about  12  feet  long  by 
closely  winding  Xo.  18  spring-brass  wire  on  a  rod  about  half  an  inch 
in  diameter.  Fasten  one  end  of  the  spiral  to  a  hook  on  the  wall,  or 
clamp  it  in  a  vise,  and  tie  short  pieces  of  bright-colored  strings  into 

several  of  the  coils.  Holding 
the  other  end  of  the  spiral  in 
the  hand,  insert  a  finger-nail  or 
knife-blade  between  two  turns 
FIG.  157.  of  the  wire  near  the  hand,  and 

pull  one  of  them  further  from 

the  other.  Suddenly  release  the  coil,  and  a  pulse  will  run  along  the 
spiral.  Each  coil  swings  to  and  fro,  the  coils  being  crowded  closely 
together  at  one  place,  and  more  widely  separated  at  another,  as  shown 
in  Fig.  157. 

Experiment  112.  —  Tightly  tie  a  sheet  of  writing  paper  over  the 
large  end  of  the  tube  used  in  Experiment  98,  and  hold  a  candle  flame 
in  front  of  the  small  end.  Tap  the  paper  diaphragm,  and  notice  the 
consequent  flickering  of  the  flame. 

183,   Waves   of    Condensation    and    Rarefaction.  —  The 

advancing  paper  diaphragm  or  other  vibrating  body 
crowds  the  layers  of  air  immediately  in  its  front,  thus 
setting  up  a  condensation  or  push  along  the  length  of  the 
tube,  as  explained  in  §  178.  When  the  paper  swings  with 


THE   NATURE   OF   SOUND,   ETC. 


211 


its  pendulum-like  motion  in  the  opposite  direction,  the 
nearest  layers  of  air  follow  it,  thus  setting  up  a  rarefac- 
tion. As  the  paper  diaphragm  continues  to  vibrate,  a 
series  of  condensations  and  rarefactions  is  sent  along  the 
tube,  as  shown  in  Fig.  158,  which  compare  with  Fig.  154. 
The  air  particles  are  crowded  unusually  at  A  and  6r,  where 
their  velocity  is  the  least,  and  are  separated  more  widely 
at  D,  where  their  velocity  is  the  greatest.  Just  as  a  water 


FIG.  158. 

wave  consists  of  two  parts,  the  crest  and  the  trough,  so  a 
sound  wave  consists  of  two  parts,  a  condensation  and  a 
rarefaction.  The  particles  in  a  sound  wave  move  with 
simple  harmonic  motion  forward  and  backward  in  the  line 
of  propagation,  and  not  across  it.  The  vibrations  are 
longitudinal,  not  transverse. 

(a)  A  series  of  complete  sound  waves,  such  as  would  be  set  up  in 
the  open  air,  consists  of  alternate  condensations  and  rarefactions 
advancing  in  the  form  of  concentric  spherical  shells,  at  the  common 
center  of  which  is  the  sounding  body.  Any  radius  of  the  sphere  is  a 
line  of  propagation  of  the  sound. 

(6)  The  distance  from  any  point  to  the  next  point  that  is  in  the 
same  phase,  as  from  condensation  to  condensation  or  from  rarefaction 
to  rarefaction,  is  a  wave-length.  The  wave  advances  one  wave-length 
in  the  time  required  for  one  vibration,  or  in  a  wave-period. 

(c)  A  sinusoidal  curve  like  that  shown  in  Fig.  156  is  commonly 
used  to  represent  a  sound  wave.  The  parts  above  the  horizontal  line 
represent  condensations,  while  the  parts  below  that  line  represent 


212 


SCHOOL   THYSICS. 


rarefactions.  Perpendicular  distances,  from  the  curve  to  the  line  A  B, 
i.e.,  ordinates,  show  the  relative  amount  of  condensation  or  rarefac- 
tion at  any  point  of  the  curve;  but  it  must  not  be  inferred  that  ampli- 
tudes are  as  great  relative  to  wave-lengths  as  would  be  indicated  by 
the  curves.  The  curve  is  merely  a  symbol  for  the  sound  wave,  not  a 
picture  of  one. 

(d)  Fig.  159  represents  apparatus  devised  by  Mach  for  the  illus- 
tration of  the  pendular  motions  of  the  particles  of  a  medium  trans- 
mitting waves  of  any  kind,  longitudinal  or  transverse,  stationary  or 
progressive.  A  wooden  framework  about  2.2  m.  long  and  1.2  m.  high 
is  arranged  to  support  17  or  more  pendulums  with  bifilar  suspensions 
0.9  m.  long.  At  the  top  of  the  frame  are  two  parallel  bars  joined  by 


FIG.  159. 

pivoted  crossbars,  after  the  manner  of  the  familiar  parallel  ruler,  and 
so  that  they  may  be  separated  about  10  cm.  One  string  of  the  bifilar 
suspension  of  each  pendulum  is  fastened  to  the  inner  face  of  the  fixed 
bar,  and  the  other  string  to  the  inner  face  of  the  movable  bar.  When 
the  two  bars  are  as  far  apart  as  possible  (as  shown  in  the  figure),  the 
balls  can  swing  lengthwise  of  the  frame ;  i.e.,  longitudinally.  When 
the  two  bars  are  brought  close  together  the  balls  can  swing  only 
transversely. 


THE   NATURE   OF   SOUND,   ETC.  213 

A  light  frame  worked  by  the  foot-lever  carries  a  wave  "pattern." 
The  holes  in  this  pattern  are  at  varying  distances  from  each  other, 
one  part  representing  a  rarefaction  and  another  part  representing  a 
condensation,  as  is  clearly  shown  in  the  figure.  When  the  pattern  is 
raised  by  the  lever,  the  pendulums  may  be  placed  in  the  holes.  When 
the  pattern  is  lowered,  the  balls  swing  longitudinally,  their  relative 
motions  representing  a  stationary  sound  wave,  such  as  the  wave  in  an 
organ-pipe,  and  giving  a  vivid  idea  of  the  alternate  condensations  and 
raref  actions. 

A  block,  shown  at  the  lower  right-hand  part  of  the  figure,  may  be 
drawn  along  the  framework  by  the  string  attached  to  it.  This  block 
has  upon  its  upper  surface  a  groove  of  such  depth  that,  as  it  is  drawn 
under  the  balls  from  one  end  of  the  row  to  the  other,  each  ball  is 
pulled  from  its  position  of  rest  and  released  as  the  block  passes  under 
it.  Thus  is  produced  the  form  of  a  progressive  wave  of  condensation 
and  rarefaction. 

The  two  bars  that  support  the  pendulums  may  be  brought  together 
so  that  the  balls  can  swing  only  transversely,  and  the  pattern  pre- 
viously used  may  be  replaced  by  the  sinusoidal  pattern  that  represents 
one  complete  wave.  Such  a  sinusoidal  pattern  is  shown  in  the  figure. 
When  this  pattern  is  raised  by  the  foot-lever  and  the  balls  placed  in 
the  holes  and  the  pattern  then  dropped,  the  pendular  motions  give  a 
clear  representation  of  a  stationary  transverse  wave. 

A  long  board,  just  wide  enough  to  reach  from  the  pattern  supports 
to  the  top  of  the  balls  may  be  placed  on  edge  so  that  all  of  the  balls 
are  pushed  about  10  cm.  to  one  side  of  their  positions  of  rest. 
When  this  board  is  drawn  endwise,  the  balls  are  successively  re- 
leased, and  the  pendular  motions  represent  a  progressive  transverse 
wave. 


CLASSROOM  EXERCISES. 

1.  State  clearly  the  difference  between  a  transverse  and  a  longitu- 
dinal wave.     Illustrate. 

2.  The  velocity  of  sound  being  given  as  1,145  feet  per  second,  what 
is  the  wave-length  of  a  tone  due  to  458  vibrations  per  second  ? 

3.  It  is  a  common  experiment  for  one  of  two  boys  in  swimming  to 
hold  his  head  under  water  while  another  at  a  distance  strikes  two 
stones  together  under  water.     The  loudness  of  the  sound  heard  by 
the  first  boy  is  painful  and  sometimes  injurious,  even  when  the  dis- 


214  SCHOOL  PHYSICS. 

tance  is  so  great  that  the  sound  would  be  scarcely  heard  in  the  air. 
Explain. 

4.  If  a  blow  is  struck  with  a  hammer  upon  one  end  of  a  long  iron 
pipe,  a  listener  at  the  other  end  may  hear  two  sounds  instead  of  one. 
Explain. 

5.  What  is  the  difference  between  the  physical  and  the  physiologi- 
cal definitions  of  the  word  "  sound  "  ? 

6.  What  is  the  difference  between  an  oscillation  and  a  vibration? 

7.  What  is  the  difference  between  a  motion  of  translation  and  one 
of  vibration  ?     Illustrate. 

8.  Why  is  the  motion  of  a  particle  of  the  medium  through  which  a 
sound  is  passing  properly  described  as  "  pendular  "  ? 

9.  How  does  a  pendular  motion  differ  from  a  simple  harmonic 
motion  ? 

10.  What  word  accurately  describes  the  curve  that  is  used  as  a 
symbol  of  a  sound  wave  ? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  wooden  rod  about  half  an  inch 
square  and  12  feet  long ;  cardboard ;  India  ink ;  drawing  instruments ; 
heavy  plank  and  blocks ;  hinge  ;  clock  spring ;  pocket  tuning-fork. 

1.  Draw  a  graphic  representation  of  a  series  of  waves  of  troughs  and 
crests  as  follows :  With  a  radius  equal  to  the  amplitude  of  vibration, 
draw  a  circle.  Draw  its  vertical  diameter,  A  I.  Beginning  at  A  or  7, 
divide  the  circumference  of  the  circle  into  any  number  of  equal  parts, 
say  16.  Through  these  divisions  draw  horizontal  lines  intersecting 
A I  at  the  points  B,  C,  D,  E,  F,  G,  and  H,  and  prolong  them  indefi- 
nitely. See  Fig.  154.  Similarly  extend  tangents  to  the  circle  at  A 
and  /.  On  the  extension  of  the  line  passing  through  E,  the  center  of 
the  circle,  lay  off  successively  16  equal  parts.  Consider  the  beginning 
of  the  first  of  these  equal  parts  as  the  origin  of  co-ordinates,  and 
number  thence  the  successive  divisions  on  the  axis  of  abscissas,  from 
1  to  16  inclusive.  Through  these  16  points,  draw  vertical  lines,  ter- 
minating the  successive  verticals  at  the  points  where  they  intersect 
the  successive  horizontal  lines.  Mark  these  successive  intersections 
1',  2',  3',  etc.,  to  15'.  Then  the  ordinates  of  V  and  T  will  be  equal  to 
EF;  those  of  2'  and  6'  will  be  equal  to  EG;  those  of  3'  and  5'  will 
be  equal  to  EH,  and  that  of  4'  will  be  equal  to  El.  The  ordinates 
of  8'  and  16'  will  be  zero.  The  ordinates  of  9'  and  15'  will  be  nega- 


THE  NATURE  OF  SOUND,  ETC.         215 

tive  and  equal  to  ED ;  those  of  10'  and  14'  will  be  negative  and  equal 
to  EC ;  those  of  11'  and  13'  will  be  negative  and  equal  to  EB;  that 
of  12'  will  be  negative  and  equal  to  EA .  Join  these  several  loci  by 
drawing  a  curve  through  them,  and  we  have  the  wavy  line  known  as 
a  sinusoidal  curve,  the  outline  of  the  wave  as  required.  What  is  the 
distance  from  O  to  16  called?  What  is  the  distance  from  4  to  4' 
called  ?  What  is  the  point  4'  called  ?  What  is  the  point  12'  called  ? 
Can  you  see  any  connection  between  the  motion  of  a  drop  of  water  in 
an  oscillatory  wave  and  the  motion  of  a  pendulum  ? 

2.  Slightly  stretch  a  solid  rubber  cord  about  0.5  cm.  in  diameter 
between  a  hook  in  the  ceiling  and  another  in  the  floor.     With  a  ruler, 
tap  the  cord  near  the  lower  end,  timing  the  blows  so  that  the  cord 
shall  vibrate  as  a  whole.     Count  the  number  of  vibrations  made  in 
60  seconds.     Repeat  the  test  twice  and  determine  the  average  of  the 
three  trials. 

Tap  the  cord  more  rapidly  until  it  vibrates  in  two  segments. 
Repeat  the  test  and  determine  as  before  the  average  number  of 
vibrations  made  in  60  seconds. 

Similarly,  make  the  cord  vibrate  in  three  and  then  in  four  seg- 
ments, recording  the  numbers  of  vibrations  as  before.  Measure  the 
length  of  the  cord  between  the  hooks,  tabulate  the  segment-lengths 
and  the  numbers  of  vibrations  per  second  for  each  of  the  four  tests. 
Determine  the  relation  between  the  segment-lengths  and  the  vibration- 
numbers. 

3.  Hold  one  end  of  a  slender  wooden  rod  between  the  teeth,  while 
another  pupil  holds  the  stem  of  a  vibrating  tuning-fork  against  the 
other  end  of  the  rod.     See  if  the  fork  is  audible  without  the  inter- 
vention of  the  rod. 

4.  Cut  a  slit  1  mm.  x  4  cm.  in  a  postal  card.     Place  a  ruler  below 
Fig.  156  and  parallel  with  the  printed  lines.     Place  the  edge  of  the 
card  against  the  edge  of  the  ruler,  so  that  the  slit  shall  be  at  right 
angles  to  the  line,  AB,  at  its  end.     AB  should  show  through  the  slit 
at  its  middle  point.     Slide  the  card  with  steady  motion  along  the 
edge  of  the  ruler,  observing  the  apparent  motion  of  the  black  line 
seen  through  the  slit.     How  does  that  apparent  motion  up  and  down 
the  slit  compare  with  the  simple  harmonic  motion  of  the  pendulum? 

5.  From  a  piece  of  stiff  cardboard,  cut  a  disk  31  cm.  in  diameter, 
and  from  its  center  draw  a  circle  0.5  cm.  in  diameter.     Divide  the 
circumference  of  this  little  circle  into  twelve  equal  parts,  and  number 
the  points  of  division  consecutively  from  1  to  12.     With  dot  1  as  a 


216 


SCHOOL  PHYSICS. 


FIG.  160. 


center,  draw  a  circle  with  a  radius  of  7.5  cm.,  using  the  pen-compasses 
and  India  ink.  With  dot  2  as  a  center,  draw  a  circle  with  a  radius  of 
7.8  cm.  With  dot  3  as  a  center,  draw  a  circle  with  a  radius  of  8.1  cm. 
Continue  to  draw  such  eccentric  circles,  using  the  numbered  dots  in 

succession  as  centers  and  in- 
creasing the  radius  by  0.3  cm. 
each  time.  Go  thus  around 
the  little  circle  twice,  when  you 
will  have  24  circles  drawn  upon 
the  cardboard,  as  indicated  in 
Fig.  160.  Cut  a  hole  exactly  at 
the  center  and  mount  the  disk 
upon  the  spindle  of  a  whirling 
table.  Cut  a  narrow  slit  about 
10  cm.  long  in  a  card,  and  hold 
it  so  that  the  slit  lies  parallel 
to  a  radius  of  the  disk  and 
close  to  it.  The  short  arcs  of 
the  circles  seen  through  the 
slit  look  like  a  series  of  dots,  each  of  which  may  be  taken  to  represent 
an  air  particle.  Still  viewing  the  dots  through  the  slit,  rotate  the  disk 
and  you  will  get  a  very  vivid  idea  of  the  way  in  which  air  particles 
actually  move  when  set  in  motion  by  a  sound  wave. 

6.  From  a  two-inch  plank,  cut  a  baseboard  about  75  x  20  cm. 
To  one  edge  of  this  base  and  about  20  cm.  from  one  end,  screw  an 
upright,  and  at  the  upper  end  of  the  upright  support  a  short  hori- 
zontal shelf,  one  edge  of  which 
shall  be  over  and  parallel  with 
the    middle   line   of    the   base- 
board.   Paste  one  end  of  a  small 
strip  of  stout  paper  to  one  end 
of  a  piece  of  glass  about  15  cm. 
long  and  10  cm.  wide,  so  that 
the  projecting  part  of  the  paper 
may  serve  as  a  handle  for  mov- 
ing the  glass,  which  is  to  be  lightly  smoked.     Provide  a  wooden 
block  shaped  like  that   shown  in  Fig.  161,  the  greatest  length  of 
which  is  about  30  cm.  long  and  the  thickness  of  which  at  the  part 
marked  a  is  about  2.5  cm.     The  several  faces  of  the  thicker  part  of 
this  block  have  holes,  into  any  one  of  which  the  handle  of  a  tuning- 


FIG.  Nil. 


THE   NATURE   OF  SOUND,   ETC. 


217 


9 

FIG.  1(>2. 


fork  may  be  driven.  The  face,  i,  carries  a  hinge  for  fastening  the 
block  to  the  baseboard,  and  near  the  end  of  a  is  a  large  screw-eye 
extending  into  the  baseboard.  Fig.  162  shows  a  pendulum  sup- 
ported from  the  edge  of  the  shelf  already  men- 
tioned. The  pendulum  is  made  of  a  straightened 
piece  of  clock-spring  with  a  lead  bullet-bob  at  the 
lower  end.  The  under  side  of  the  bob  carries  a 
style.  This  pendulum  will  vibrate  across  a  line 
drawn  along  the  middle  of  the  baseboard.  Place 
the  smoked  glass  on  the  baseboard  so  that  its 
length  shall  be  parallel  with  the  length  of  the 
board,  and  so  that  the  pendulum  shall  hang  near 
the  end  that  carries  the  paper  strip.  Drive  the 
handle  of  the  tuning-fork  into  the  hole  in  the 
block  at  the  face  marked  t,  and  fasten  the  block 
at  the  other  end  of  the  smoked  glass  so  that  the 
style  at  the  end  of  the  fork  shall  come  as  near  as  possible  to  the 
style  of  the  pendulum,  and  shall  swing  parallel  with  it  when  prong 
and  pendulum  are  both  in  motion.  Adjust  the  height  of  the  shelf 
so  that  the  pendulum  wijl  be  long  enough  to  make  between  100 
and  150  complete  oscillations  per  minute.  Then  adjust  the  pendulum 
at  the  clamp  on  the  edge  of  the  shelf  so  that  the  style  carried  by  the 
bob  may  just  touch  the  glass  and  cut  a  line  on  its  smoked  surface. 
Accurately  count  the  number  of  vibrations  that  the  adjusted  pendu- 
lum makes  in  a  minute.  Loosen  the  screw  at  the  further  end  of  the 
block  that  carries  the  fork,  and  adjust  the  height  so  that  the  style  at 
the  end  of  the  prong  just  grazes  the  surface  of  the  glass.  Tack  a  thin 
strip  of  wood  at  the  long  edge  of  the  glass  to  serve  as  a  guide  for  the 
latter.  Set  pendulum  and  fork  in  vibration  and  quickly  draw  the 
glass  lengthwise.  From  the  two  traces  on  the  glass,  count  the  num- 
ber of  vibrations  of  the  fork  that  correspond  to  one  vibration  of  the 
pendulum,  and  thence  compute  the  vibration-number  of  the  fork. 


218  '  SCHOOL   PHYSICS. 


II.    VELOCITY,   REFLECTION,   AND   REFRACTION 
OF   SOUND. 

Experiment  113.  —  Provide  three  similar  rubber  tubes,  each  about 
3  m.  long;  fill  one  of  them  with  sand,  and  with  equal  tension  stretch  the 
three  side  by  side,  suspended  between  supports  at  their  ends.  Strike 
the  two  empty  tubes  simultaneously  with  a  ruler  and  near  one  end ; 
notice  that  a  wave  runs  along  each  tube  to  the  other  end  where  it  is 
reflected;  the  waves  return  to  the  starting  point  at  practically  the 
same  time;  they  travel  with  equal  velocities.  Increase  the  tension 
of  one  of  the  tubes  and  repeat  the  experiment.  The  increase  of  the 
elastic  force  increases  the  velocity  of  the  wave.  Similarly,  send  a 
wave  along  the  sand-filled  tube,  and  notice  that  the  waves  travel  per- 
ceptibly more  slowly  in  the  heavier  tube. 

184.  The  Velocity  of  Sound  depends  upon  two  considera- 
tions, —  the  elasticity  and  the  density  of  the  medium. 
It  varies  directly  as  the  square  root  of  the  elasticity,  and 
inversely  as  the  square  root  of  the  density. 


(a)  In  solids,  elasticity  is  measured  by  the  modulus  of  elasticity 
(E),  which  is  the  reciprocal  of  the  coefficient  of  elasticity  (e).  In 
liquids  and  gases,  elasticity  is  measured  by  the  resistances  they  offer 
to  compression. 

(6)  The  velocity  of  the  wave  motion  may  be  found  by  multiplying 
the  wave-length  by  the  number  of  vibrations  per  second,  or  the  wave- 
length may  be  found  by  dividing  the  velocity  by  the  number  of  vibra- 
tions. 

(c)  Careful  experiment  has  established  the  fact  that  the  velocity  of 
sound  in  air  at  the  freezing  temperature  (0°  C.  or  32°  F.)  is  about  332  m., 
or  1,090  feet  per  second.  Oxygen  is  sixteen  times  as  dense  as  hydro- 
gen. Under  the  same  pressure,  the  elasticity  is  the  same ;  hence, 
sound  travels  four  times  as  fast  in  hydrogen  as  it  does  in  oxygen.  A 
change  of  pressure  on  a  gas  will  change  elasticity  and  density  equally, 
and,  therefore,  will  not  affect  the  velocity  of  sound  transmitted  by  the 
gas.  If  a  confined  portion  of  any  gas  is  heated,  its  elasticity  is  in- 


VELOCITY,    REFLECTION,    AND   REFRACTION.          219 

creased  without  any  change  of  density.  Hence,  a  rise  of  temperature 
without  barometric  change  increases  the  velocity  of  sound  in  the  air. 
The  added  velocity  is  about  0.6  m.,  or  2  feet  for  each  degree  that  the 
centigrade  thermometer  rises ;  or  0.33  m.  or  1.12  feet  for  each  degree 
that  the  Fahrenheit  thermometer  rises. 

(rf)  Owing  to  the  high  elasticity  of  liquids  and  solids  as  compared 
with  their  densities,  they  transmit  sound  with  great  velocities.  In 
water  at  8°  C.,  sound  travels  at  the  rate  of  4,708  feet  per  second,  and 
the  velocity  is  considerably  affected  by  changes  of  temperature;  in 
glass,  the  velocity  is  14,850  feet,  and  in  iron  it  is  16,820  feet ;  in  lead, 
a  metal  of  high  density  and  low  elasticity,  the  velocity  of  sound  is 
4,030  feet  per  second. 

Reflection. 

Experiment  114.  —  Repeat  Experiment  110,  and  notice  that  the 
waves  successively  started  by  the  hand  are  turned  back  at  the  other 
end  of  the  rope  and  meet  the  advancing  waves.  When  any  part  of 
the  rope  is  equally  urged  in  opposite  directions  by  a  direct  and  a  re- 
flected wave,  the  resultant  of  the  two  forces  is  zero,  and  the  rope  at 
that  point  remains  at  rest. 

Experiment  115.  —  Slip  the  loops  at  the  ends  of  the  wire  spiral  used 
in  Experiment  111  over  hooks  screwed  into  the  sides  of  two  boxes. 
Separate  the  boxes  so  as  to  support  and  slightly  stretch  the  spiral, 
fastening  the  boxes  by  nailing  them  down  or  by  loading  them  with 
sand.  Start  a  pulse  in  the  spiral,  and  notice  that  the  wave  runs  to 
the  other  end,  is  turned  back  or  reproduced  in  the  same  medium, 
moves  along  the  spiral  to  its  starting  point,  and  so  continues  its  jour- 
neys to  and  fro  until  its  energy  is  dissipated.  It  looks  as  though  a 
wave  motion  might  be  reflected  (§  76)  as  well  as  a  motion  of  trans- 
lation. 

Experiment  116.  — Hold  a  lamp  reflector  or  other  large  concave 
mirror  directly  facing  the  sun,  so  as  to  bring  the  rays  of  light  to  a 
focus.  Move  a  piece  of  paper  until  you  find  the  place  where  a  spot 
on  the  paper  is  most  brilliantly  illuminated  by  the  reflected  rays,  and 
measure  the  distance  of  this  focus,  F,  from  A,  the  center  of  the  re- 
flector (see  Fig.  163).  At  some  point,  W,  between  F  and  C,  the  center 
of  curvature  of  the  reflector,  hang  a  loud-ticking  watch,  and  hunt  for 
the  point,  X,  at  which  the  ear  can  most  distinctly  hear  the  ticking. 


220 


SCHOOL   PHYSICS. 


FIG.  163. 


Use  a  glass  funnel  as  an  ear-trumpet.  Keep  watch  and  ear  in  these 
positions,  and  have  the  reflector  removed.  The  ticking  will  be  faint 
or  inaudible. 

185.  Reflection 
of  Sound.  —  When 
a  sound  wave 
strikes  an  obsta- 
cle,  it  is  reflected 
in  obedience  to  the 
principle  given  in 
§  76.  Fig.  164 
represents  two 

parabolic  reflectors,  mn  and  op.  It  is  a  peculiarity  of 
such  reflectors  that  rays  starting  from  the  focus,  as  F, 
will  be  reflected  as  parallel  rays, 
and  that  parallel  rays  falling  upon 
such  a  reflector  will  converge  at 
the  focus,  as  P '.  Hence,  two  such 
reflectors  may  be  placed  in  such 
a  position  that  sound  waves 
starting  from  one  focus  shall, 
after  two  reflections,  be  converged 
at  the  other  focus.  By  such  means,  the  ticking  of  a 
watch  may  be  made  audible  at  a  distance  of  two  or  three 
hundred  feet.  Two  reflectors  so  placed  are  said  to  be  con- 
jugate to  each  other.  This  principle  underlies  the  phe- 
nomena of  whispering  galleries. 

186.  An  Echo  is  a  sound  repeated  by  reflection  so  as 
to  be  heard  again  at  its  source.  If  the  direct  and 
reflected  sounds  succeed  each  other  with  great  rapidity, 
as  will  be  the  case  when  the  reflecting  surface  is  near,  the 


\L 


FIG.  1(54. 


VELOCITY,    REFLECTION,   AND   REFRACTION. 


221 


echo  obscures  the  original  sound  and  is  not  heard  dis- 
tinctly. Such  indistinct  echoes  often  interfere  with 
distinct  hearing  in  large  halls  and  churches.  Multiple 
or  tautological  echoes  are  due  either  to  independent  re- 
flections by  bodies  at  different  distances,  or  to  successive 
reflections,  as  between  parallel  walls. 

(a)  The  time  interval  between  a  sound  and  its  echo  is  the  time 
required  for  a  sound  to  travel  twice  the  space  interval  between  the 
source  of  the  sound  and  the  reflecting  body.  Suppose  that  a  person 
can  distinctly  pronounce  five  syllables  in  a  second.  While  one  sylla- 
ble is  being  spoken,  the  sound  waves  that  constitute  the  first  part  of 
the  syllable  will  have  traveled  one-fifth  of  1,120  feet  or  224  feet.  If 
these  waves  are  to  be  brought  back  to  the  ear  of  the  speaker  imme- 
diately after  the  syllable  is  completed,  the  reflecting  surface  should 
be  about  112  feet  distant.  If  it  is  nearer  than  this,  the  reflected  sound 
will  return  before  the  articulation  is  complete  and  confusedly  blend 
with  it.  If  the  reflector  is  224  feet  distant,  there  will  be  time  to 
pronounce  two  syllables  before  the  reflected  wave  returns.  The 
echo  of  both  syllables  may  then  be  heard ;  and  so  on. 

Refraction. 

Experiment  117.  —  Fill  with  carbon  dioxide  a  large  rubber  toy  bal- 
loon or  other  double- 
convex  lens  having  easily 
flexible  walls.  Suspend 
a  watch,  and  place  your- 
self so  that  you  can  just 
hear  its  ticking.  Have 
the  gas-filled  lens  moved 
back  and  forth  in  the 
line  between  watch  and 
ear  until  the  ticking  is 
much  more  plainly  heard. 
Use  a  glass  funnel  as  an 
ear-trumpet. 

187.  Refraction  of  Sound.  —  As  explained  in  §  183  (a), 
the  lines  of  propagation  of  sound  are  ordinarily  radial  or 


FIG. 


222  SCHOOL  PHYSICS. 

divergent.  When  such  waves  pass  obliquely  from  one 
medium  to  another  of  different  density,  the  line  of  propa- 
gation is  bent,  as  will  be  more  fully  explained  in  the 
chapter  on  Light.  This  bending  of  the  lines  of  propagation 
is  called  refraction.  Such  lines  may  be  made  less  diver- 
gent or  even  converging,  as  in  Experiment  117,  and  the 
energy  of  the  waves  concentrated  at  a  focus. 

CLASSROOM  EXERCISES. 

1.  If  18  seconds  intervene  between  the  flash  and  report  of  a  gun, 
what  is  its  distance,  the  temperature  being  0°  C.V 

2.  Steam  was  seen  to  escape  from  the  whistle  of  a  locomotive,  and 
the  sound  was  heard  7  seconds  later.     The  temperature  being  15°  C., 
how  far  was  the  locomotive  from  the  observer  ? 

3.  What  is  the  length  of  sound  waves  propagated  through  air  at  a 
temperature  of  15°  C.  by  a  tuning-fork  that  vibrates  224  times  per 
second  ? 

4.  Determine  the  temperature  of  the  air  when  the  velocity  of  sound 
is  1,150  feet  per  second. 

5.  Why  will  an  open  hand  or  a  palm-leaf  fan  held  back  of  the  ear 
often  aid  a  partly  deaf  person  in  hearing  a  speaker  ? 

6.  A  shot  is  fired  before  a  cliff  and  the  echo  heard  6  seconds  later. 
The  temperature  being  15°  C.,  determine  the  distance  of  the  cliff. 

7.  A  musical  instrument  makes  1,100  vibrations  per  second.    Under 
what  conditions  will  the  sound  waves  be  each  a  foot  long  ? 

8.  How  many  vibrations  per  second  are  necessary  for  the  formation 
of  sound  waves  4  feet  long,  the  velocity  of  sound  being  1,120  feet? 
Determine  the  temperature  at  the  time  of  the  experiment. 

9.  Taking  the  velocity  of  sound  as  332  m.,  determine  the  length  of 
the  waves  produced  by  a  body  vibrating  830  times  per  second. 

10.  When  the  velocity  of  sound  is  1,128  feet,  determine  the  rate  of 
vibration  of  the  vocal  cords  of  a  man  whose  voice  sets  up  waves  12 
feet  long. 

11.  A  person  stands  before  a  cliff  and  claps  his  hands  and  hears  an 
echo  in  |  of  a  second.     Determine  the  distance  of  the  cliff  from  the 
man. 

12.  A  sportsman  fires  his  gun  and  2£  seconds  later  hears  its  report 


VELOCITY,  REFLECTION,  AND  REFRACTION.    223 

the  second  time.     The  temperature  being  0°  C.,  how  far  away  is  the 
reflecting  surface  ? 

13.  A  stone  is  dropped  down  the  shaft  of  a  mine  and  5  seconds 
later  is  heard  to  strike  the  bottom.     The  temperature  being  15°  C., 
what  is  the  depth  of  the  mine  ? 

14.  Why  does  sound  travel  more  rapidly  through  the  iron  of  a  pipe 
than  it  does  through  the  air  contained  in  the  pipe? 

15.  From  the  cyclopedia,  cull  the  story  of  the  prison  built  by  Dio- 
nysius,  the  Syracusan  tyrant,  and  explain  its  remarkable   acoustic 
properties. 

16.  Two  single-stroke  electric  bells  on  the  same  circuit  are  made 
to  strike  5  times  a  second.     When  the  bells  are  at  the  same  distance 
from  the  hearer,  5  strokes  per  second  are  heard ;  when  one  of  them 
is  about  112  feet  further  away  than  the  other,  10  strokes  per  second 
are  heard ;  and  when  one  of  them  is  about  22-4  feet  further  away  than 
the  other,  only  5  strokes  per  second  are  heard.     Explain. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  seconds  pendulum;  spy  glass  or  opera 
glass;  heavy  hammer;  long  measuring  tape;  thermometer;  two  pis- 
tols ;  two  or  more  good  watches ;  cardboard ;  toy  trumpet ;  a  few 
lengths  of  tin  water-spout. 

1.  Let  two  pupils,  A  and  B,  take  positions  about  900  feet  apart,  so 
that  each  can  see  the  other.  Let  A  set  up  a  seconds  pendulum  with 
a  heavy  bob  painted  white,  so  that  it  shall  swing  across  the  line 
extending  from  him  to  B.  Drive  a  stake  beneath  the  pendulum  bob, 
or  indicate  its  lowest  position  in  some  other  way  that  may  be  seen  by 
B.  Swing  the  pendulum,  and,  just  as  the  pendulum  passes  the  verti- 
cal, strike  a  board,  stone,  or  anvil  with  a  hammer  that  carries  a  white 
cloth,  so  that  its  motion  may  be  easily  visible.  B  observes  these 
motions  through  a  spy  glass  and  shifts  his  position  from  time  to  time, 
signaling  for  other  hammer  strokes,  until  his  distance  from  A  is  such 
that  the  sound  produced  when  the  pendulum  passes  the  vertical  in 
one  direction  is  heard  when  the  pendulum  passes  the  vertical  in  the 
other  direction.  Mark  the  position  of  B.  Measure  the  distance 
between  A  and  B,  and  note  the  reading  of  the  thermometer.  If  the 
wind  is  not  blowing,  this  distance  roughly  indicates  the  velocity  of 
sound  in  air  at  the  observed  temperature.  It  will  be  well  to  check 
the  result  obtained  by  reversing  the  experiment.  Let  A  swing  the 
pendulum.  Let  B  watch  it  until  he  feels  the  motions,  and  then  strike 


224  SCHOOL  PHYSICS. 

a  blow  just  as  the  pendulum  passes  the  vertical.  If  A  does  not  hear 
the  sound  just  as  the  pendulum  next  passes  the  vertical,  let  him 
signal  .B  to  come  nearer  or  go  further  away,  continuing  the  work 
until  the  sound  moving  from  B  to  A  comes  in  on  time.  Let  B 
measure  the  distance  between"  his  two  stations,  and  thence  determine 
the  distance  of  his  second  position  from  A.  The  average  of  the  two 
distances  between  A  and  .B  may  be  taken  as  the  velocity  of  sound  in 
still  air  at  the  temperature  observed.  If  your  result  differs  much 
from  the  velocity  as  computed  from  the  data  recorded  in  §  184  (c), 
you  may  know  that  your  work  has  not  been  well  done. 

NOTE.  —  Exercises  1  and  2  may  not  be  practicable  in  the  immediate 
vicinity  of  a  city  school,  but  it  is  well  worth  the  effort  to  make  a  Sat- 
urday scientific  class-excursion  into  the  country,  for  the  purpose  of 
executing  them.  If  the  experiments  are  performed  in  the  cool  air  of 
a  frosty  morning,  and  repeated  in  the  warmer  air  of  early  afternoon, 
a  change  in  the  velocity  of  the  sound  will  be  observed. 

2.  Place  two  pupils,  C  and  Z>,  each  of  whom  has  a  pistol  and  a 
watch,  and  knows  how  to  take  care  of  them,  a  long  distance  apart, 
but  in  sight  of  each  other.     Let  half  of  the  pupils  who  have  watches 
accompanv  C;  the  others  who  have  watches  should  go  with  D.     Let 
C  fire  his  pistol,  D  and  his  party  noting  the  interval   between  the 
appearance  of  the  flash  and  the  hearing  of  the  report.     Take  the 
average    of   the    observations   made   by  the    different    members    of 
the  party,  excluding  any  observation  that  differs  very  widely  from 
most  of  the  others.     Then  let  D  fire  his  pistol  while  C  and  his  party 
observe  the  interval  and  determine  their  average.     Measure  the  dis- 
tance between  the  stations  occupied  by  C  and  D,  and  note  the  read- 
ing of  the  thermometer.     Record  the  average  of  the  two  averages  as 
the  time  required  for  sound  to  travel  that  distance  at  that  tempera- 
ture.    From  such  data  compute  the  velocity  of  sound  per  second  under 
the  conditions  of  the  experiment. 

3.  On  opposite  sides  of  the  center  of  a  disk  of  cardboard  about  15 
inches  in  diameter,  cut  out  two  sectors,  as  shown  in  Fig.  166.     Mount 
the   disk   on   a  whirling  table.      Sit  beside  the  apparatus,  so  as  to 
turn  the  driving  wheel  with  one  hand,  and  with  the  other  hold  a.  toy 
trumpet  so  that  its  axis  shall  be  inclined  to  the  surface  of  the  disk, 
about  midway  between  center  and  circumference.     Rotate  the  disk 
steadily  and  sound  the  trumpet  at  the  same  time.     Let  other  pupils 
take  positions  in  a  distant  part  of  the  room,  as  indicated  by  the  law  of 
reflected  motion,  so  that  the  sound  waves  from  the  trumpet  reflected 


CHARACTERISTICS   OF  TONES.  225 

by  the  disk  will  reach  their  ears.  When  the  sectors  pass  before  the 
mouth  of  the  trumpet,  the 
sound  will  become  softer, 
and  when  the  cardboard  re- 
flector passes,  the  sound  will 
become  stronger.  Record  a 
description  and  explanation 
of  the  experiment. 

4.  On   a   table  like  that 
shown  in  Fig.  45,  lay  two 

tin  tubes,  each  about  150  cm. 

,'  .     ,.  FIG.  166. 

long  and  10  cm.  in  diameter. 

A  few  lengths  of  water-spout  will  answer.  The  axes  of  the  tubes 
should  lie  on  radial  lines  (like  BA  and  BC)  that  make  equal  angles 
with  the  radius,  BD,  drawn  perpendicular  to  the  reflecting  surface 
at  B.  If  you  have  no  such  table,  draw  the  radial  lines  on  any 
table-top,  and  properly  place  a  piece  of  glass,  as  at  B,  to  serve  as  a 
reflector.  Suspend  a  watch  at  the  outer  end  of  one  of  the  tubes  and 
hold  the  ear  at  the  outer  end  of  the  other  tube.  Notice  the  intensity 
of  the  sound  caused  by  the  ticking  of  the  watch.  Shift  the  inner 
end  of  one  of  the  tubes  from  its  position.  Listen  again  and  notice 
the  relative  intensity  of  the  sound. 


III.    CHAKACTEEISTICS   OF  TONES. 

188.  Differences  in  Tones.  —  Sound  waves  differ  in 
respect  to  amplitude,  length,  and  form.  These  differences 
in  the  waves  give  rise  to  corresponding  differences  in  the 
sensations  that  they  produce.  Variations  in  amplitude 
correspond  to  differences  in  intensity  or  loudness  ;  differences 
in  wave-length  correspond  to  differences  in  pitch  ;  differences 
in  wave-form  correspond  to  differences  in  timbre  or  musical 
quality. 

Intensity. 

Experiment  118.  —  Set  a  tuning-fork  in  feeble  vibration  by  striking 
it  gently ;  the  sound  that  you  hear  will  be  faint.     Strike  the  fork  a 
15 


226  SCHOOL  PHYSICS. 

harder  blow ;  its  prongs  will  vibrate  with  more  energy  and  the  sound 
that  you  hear  will  be  louder.  Gently  pluck  a  guitar  string;  it  vibrates 
to  and  fro  across  its  place  of  rest,  striking  feeble  blows  upon  the  air 
and  sending  sound  waves  to  the  ear.  Pluck  the  same  string  more 
vigorously ;  it  vibrates  with  greater  amplitude,  striking  the  air  with 
greater  energy  and  sending  to  the  ear  sound  waves  of  greater  intensity 
than  before. 

189.  Intensity   and    Amplitude.  —  The    intensity    of   a 
sound  depends  primarily  upon  the  energy  of  vibration  of 
the  sonorous  body,  and  thence  on  the  amplitude  of  the 
vibrating  particles  of  the  sound  medium.     The  greater 
the  amplitude,  the  greater  the  energy  and  the  louder  the 
sound. 

(a)  If  the  amplitude  of  the  vibration  of  a  sonorous  body  is  doubled, 
the  velocity  with  which  it  swings  will  be  doubled,  for  the  vibrations 
are  as  strictly  isochronous  as  the  oscillations  of  a  pendulum.  Since 
energy  varies  as  the  square  of  the  velocity,  it  follows  that  the  intensity 
of  sound  varies  as  the  square  of  the  amplitude.  Since  energy  varies  as 
the  mass,  it  follows  that  the  intensity  of  sounds  generated  in  gases  of 
little  density  (see  Experiments  102  and  103)  will  have  less  intensity 
than  sounds  generated  in  heavier  gases  like  air  and  carbon  dioxide. 

(&)  If  a  smoked  glass  is  drawn  very  slowly  under  a  style  carried 
by  a  prong  of  a  vibrating  tuning-fork,  as  shown  in  Fig.  150,  the  soot 
will  be  scraped  from  the  glass  and  the  area  thus  cleaned  will  be  tri- 
angular. As  the  sound  of  the  fork  grows  feebler,  the  swings  of  the 
prong  become  shorter  and  the  trace  tapers  off. 

Experiment  119.  —  Whisper  into  one  end  of  a  length  (50  feet)  of 
garden  hose.  A  person  listening  with  his  ear  at  the  other  end  of  the 
hose  can  distinctly  hear  what  is  said  although  the  sound  is  inaudible 
to  a  person  holding  the  middle  of  the  hose. 

190.  Intensity  and  Distance.  —  In  the  open  air,  a  sound 
wave  expands  as  a  spherical  shell,  and  its  energy  is  dis- 
tributed among  the  increasing  number  of  air  particles  that 
constitute   these   successive   shells  or  spherical  surfaces. 
This  number  of  air  particles  varies  as  the  square  of  the 


CHARACTERISTICS   OF  TONES.  227 

radius  of  the  sphere.  The  energy  of  any  given  number  of 
these  air  particles  must,  therefore,  vary  inversely  as  the 
square  of  such  radius ;  in  other  words,  the  intensity  of  sound 
varies  inversely  as  the  square  of  the  distance  from  the  sonorous 
body. 

(a)  If  the  sound  wave  is  not  allowed  to  expand  as  a  spherical 
shell,  its  energy  cannot  be  thus  diffused  and  its  intensity  will  be 
conserved.  Hence,  the  efficiency  of  speaking-tubes  and  speaking- 
trumpets. 

(6)  The  law  above  given  is  true  only  when  the  distance  is  so  great 
in  comparison  with  the  dimensions  of  the  sounding  body  that  the 
latter  may  be  considered  a  center  from  which  sound  waves  proceed 
along  radial  lines.  A  person  10  feet  from  a  passing  railway  train 
does  not  hear  a  sound  four  times  as  loud  as  that  heard  by  a  person 
20  feet  from  the  train. 

Experiment  120.  —  Strike  a  tuning-fork  held  in  the  hand.  Notice 
the  feeble  sound.  Strike  the  fork  again  and  place  the  end  of  the 
handle  upon  a  table.  The  loudness  of  the  sound  heard  is  remarkably 
increased. 

Experiment  121.  —  Strike  the  fork  and  hold  it  near  the  ear,  count- 
ing the  number  of  seconds  that  you  can  hear  it.  Strike  the  fork 
again  with  equal  force ;  place  the  end  of  the  handle  on  the  table  and 
count  the  number  of  seconds  that  you  can  hear  it. 

191.  Intensity  and  Area.  —  When  a  vibrating  body  is 
small  or  thin,  the  particles  of  the  air  readily  flow  around 
it  instead  of  being  set  into  vibration  by  it.  Hence,  the 
sound  of  a  small  tuning-fork  is  feebler  than  that  of  a  large 
one.  When  the  sonorous  lody  has  a  large  surface,  its  vibra- 
tions set  up  well-marked  condensations  and  rarefactions,  and 
the  consequent  sound  is  correspondingly  intense. 

(a)  In  the  sonometer,  piano,  violin,  guitar,  etc.,  the  sound  is  due 
more  to  the  vibrations  of  the  resonant  bodies  that  carry  the  strings 
than  to  the  vibrations  of  the  strings  themselves.  The  strings  are  too 
thin  to  impart  enough  motion  to  the  air  to  be  sensible  at  any  con- 


228  SCHOOL  PHYSICS. 

siderable  distance ;  but  as  they  vibrate,  their  tremors  are  carried  by 
the  bridges  to  the  material  of  the  sounding  apparatus  with  which  they 
are  connected.  These  larger  surfaces  throw  larger  masses  of  air  into 
vibration  and  thus  greatly  intensify  the  sound.  It  necessarily  follows 
that  the  energy  of  the  vibrating  body  is  sooner  exhausted. 

(6)  The  intensity  of  tones  is  also  affected  by  resonance  and  inter- 
ference, as  will  be  subsequently  explained. 


Pitch. 

Experiment  122.  —  Draw  a  finger-nail  across  the  tips  of  the  teeth 
of  a  comb,  slowly  the  first  time  and  rapidly  the  second  time.  Xotice 
the  difference  in  the  sounds  produced.  If  one  is  louder  than  the 
other,  is  that  the  only  difference? 

Experiment  123.  —  The  Savart  wheel,  shown  hi  Fig.  167,  consists 
of  a  heavy  metal  toothed  wheel  that  may  be  put  in  rapid  revolution 
by  pulling  a  cord  wound  upon  its  axis.  Set 
such  a  wheel  in  rapid  motion  and  hold  the  edge 
of  a  card  against  its  teeth.  As  the  speed  of  the 
wheel  diminishes,  the  shrill  tone  produced  by 
the  rapid  vibrations  of  the  card  correspondingly 
falls  in  pitch. 

Experiment  124.  —  From  a  piece  of  stiff  card- 
board, cut  a  disk  8|  inches  in  diameter.     From 
FIG.  167?"  *he  same  center,  draw  four  circles  with  radii  of 

2£  inches,  2f  inches,  3|  inches,  and  3f  inches 
respectively.  Divide  the  inner  of  these  circumferences  into  24  equal 
parts,  the  second  into  30,  the  third  into  36,  and  the  fourth  into  48. 
At  each  division,  punch  a  T3g-inch  (5  mm.)  hole.  Cut  a  hole  at  the 
center  and  mount  the  perforated  disk  on  the  spindle  of  a  whirling 
table,  and  you  have  a  simple  .form  of  the  siren.  See  Fig.  168. 

Rotate  the  disk  slowly,  blowing  meanwhile  through  a  tube  of  about 
TVinch  bore,  the  nozzle  of  the  tube  being  held  opposite  the  interior 
ring  of  holes.  As  each  successive  hole  comes  before  the  end  of  the 
tube,  a  puff  of  air  goes  through  the  disk.  As  the  speed  of  the  disk 
increases,  the  puffs  become  more  frequent,  and  finally  blend  into  a 
whizzing  sound  in  which  the  ear  can  detect  a  smooth  tone.  As  the 
disk  is  given  an  increasing  velocity,  this  tone  rises  in  pitch.  With  a 


CHARACTERISTICS   OF    TONES. 


229 


given  rate  of  rotation  of  the  apparatus,  the  pitch  will  rise  as  the  tube 
is  moved  outward  in  succession  from  the  inner  to  the  outer  circle  of 
perforations.      Does    it  not 
appear  that  the  pitch  of  a 
sound    rises    with    the    fre- 
quency of  the  vibrations  that 
produce  it? 

192.  Pitch  is  the  char- 
acteristic of  a  sound  or 
tone  by  which  it  is  rec- 
ognized as  acute  or 
grave,  high  or  low.  It 
depends  upon  the  rapid- 
ity of  the  vibrations  by 
which  the  sound  is 
produced ;  the  more 
rapid  the  vibrations,  the 
higher  the  pitch. 

(a)  Since,  in  a  given  me- 
dium, all  sounds  travel  with 
the  same  velocity,  the  rate 
of  vibration  determines  the 
wave-length.  If  the  sounding  body  vibrates  224  times  per  second, 
224  waves  will  be  started  each  second.  If  the  velocity  of  the  sound 
is  1,120  feet,  the  total  length  of  these  224  waves  must  be  1,120  feet, 
or  the  length  of  each  wave  must  be  5  feet.  If  another  body  vibrates 
twice  as  fast,  it  will  crowd  twice  as  many  waves  into  the  1,120  feet ; 
each  wave  will  be  only  2$  feet  long.  Thus,  wave-length  may  be  used 
to  measure  pitch ;  the  greater  the  wave-length,  the  lower  the  pitch. 

(6)  If  the  sounding  body  and  the  listening  ear  approach  each 
other,  the  sound  waves  will  beat  upon  the  ear  with  greater  rapidity. 
This  is  equivalent  to  increasing  the  rapidity  of  vibration  of  the  sound- 
ing body.  The  opposite  holds  true  when  the  sounding  body  and  the 
ear  recede  from  each  other.  This  explains  why  the  pitch  of  the  whistle 
of  a  railway  locomotive  is  perceptibly  higher  when  the  train  is  rapidly 
approaching  the  observer  than  when  it  is  rapidly  moving  away  from 
him. 


FIG.  168. 


230  SCHOOL  PHYSICS. 

193.  The  Range  of  Hearing  of  different  persons  varies. 
The  lower  limit  for  'most  persons  is  probably  represented 
by  about  30  vibrations  per  second,  although  some  experi- 
menters place  it  at  16  vibrations.     Similarly,  the  upper 
limit  varies  from  38,000  to  41,000  vibrations  per  second. 
Tones  of  musical  value  lie  between  the  limits  of  27  and 
4,000  vibrations  per  second. 

(a)  Everybody  understands  the  differences  in  the  range  of  the 
human  voice,  that  one  can  sing  bass  and  another  one  soprano,  the  dif- 
ference depending  upon  the  rate  of  vibration  of  the  vocal  cords.  It 
is  equally  true,  but  not  equally  well  known,  that  some  persons  are 
unable  to  hear  low  sounds  that  are  distinctly  audible  to  most  persons, 
while  the  hearing  apparatus  of  others  is  unable  to  respond  to  sounds 
of  high  pitch  or  short  wave-length,  which  are  easily  heard  by  the 
greater  number.  Some  persons  whose  hearing  is  considered  fairly 
sensitive  have  never  heard  the  shrill  chirping  of  the  cricket. 

194.  An  Interval  is  the  difference  or  distance  in  pitch 
between  two  tones,  and  is  described  by  the  ratio  between  the 
vibration-numbers  of  the  two  tones.     Thus,  the  interval  of 
an  octave  is  represented  by  the  ratio  2  :  1 ;  a  fifth,  3:2; 
a  fourth,  4  :  3  ;  a  major  third,  5:4;  and  a  minor  third, 
6:5. 

195.  A  Musical  Scale  is  a  definite,  standard  series  of 
tones  for  artistic  purposes,  and  lying  within  a  limiting 
interval.     In  constructing  such  a  series,  the  first  step  is 
the  adoption  of  such  a  limiting  interval  for  the  division 
of  the  possible  range  of  tones  into  convenient  sections  of 
equal  length.     In  modern  music,  this  limiting  interval  is 
the  octave. 

196.  The  Gamut.  —  Starting  from  any  tone  arbitrarily 
chosen,  and  called  the  keynote,  the  interval  of  an  octave 


CHARACTERISTICS  OF   TONES. 


231 


may  be  traversed  by  seven  definite  steps,  thus  giving  a 
series  of  eight  tones  that  are  very  pleasing  to  the  ear. 
The  eighth  tone  of  this  group  becomes  the  first  tone  (i.e., 
the  keynote)  of  the  group  or  octave  above.  The  inter- 
vals between  these  tones  are  not  equal,  as  will  soon  appear 
more  clearly.  This  familiar  series  of  eight  tones  is  called 
the  gamut  or  major  diatonic  scale.  The  series  may  be 
repeated  in  either  direction  to  the  limits  of  audible  pitch. 
The  names  and  relative  vibration-numbers  of  these  tones, 
and  the  intervals  between  them,  are  as  follows  :  — 


Relative 
Absolute 
Syllables 
Relative 
Vibration 

M 

n 

^ 

I 

BE 

m      9 

;        1 

1         m 

ff 

-1  1 

8 
C4 

do 

48 

2 

*7 
names    

J-    *     ' 

123 
C3     D3     E3 
do     re    mi 
24     27     30 

1       I      1 

4 

F3 
fa 
32 

f 

i 

5       6-7 
G3    A3    B3 
sol     la     si 
36     40     45 

t     *    ¥• 

names    

vibration-  numbers    . 
i-ratios  

Intervals 


t 


(a)  The  initial  tone  or  keynote  of  such  a  series  may  have  any 
number  of  vibrations,  and  whatever  pitch  is  assigned  to  C,  the  num- 
ber of  vibrations  of  any  tone  may  be  found  by  multiplying  the 
vibration-number  for  C  by  the  vibration-ratios  given  above.  Physi- 
cists assign  to  C3,  sometimes  called  "  middle  C,"  256  vibrations  per 
second  (256  =  28).  Musicians  and  makers  of  musical  instruments  in 
this  country  and  Europe  have  adopted  the  "international  pitch," 
which  gives  for  standard  A$,  435  vibrations  per  second.  This  cor- 
responds to  258.6  vibrations  for  C3  (§  198). 

(6)  When  two  tones  with  vibration-numbers  as  1 : 2  are  sounded 
together,  the  character  of  the  combination  is  the  same  as  that  of 
either  tone  alone.  It  is  the  interval  most  readily  produced  by  the 
human  voice,  and  seems  to  have  a  foundation  in  nature ;  such  an 
interval  is  called  an  octave.  When  three  tones  with  vibration- 
numbers  as  4:5:6  are  sounded  together  (e.g.,  C,  E,  (7),  a  new 


232  SCHOOL  PHYSICS. 

quality  seems  to  be  added,  and  the  combination  produces  a  very 
pleasing  sensation.  The  tones  are  in  harmony,  or  in  accord  with 
each  other.  Such  simultaneous  sounding  of  three  or  more  concordant 
tones  constitutes  a  chord,  of  which  there  are  several  kinds.  The  three 
tones  above  mentioned  (i.e.,  C,  E,  G)  constitute  a  major  chord.  A 
combination  of  three  tones  with  vibration-numbers  as  10  :  12  :  15 
(e.g.,  E,  0,  B)  constitute  a  minor  chord. 

197.  Diatonic  Scales.  —  The  major  diatonic  scale  is  built 
upon  three  major  chords,  and  the  minor  diatonic  scale  upon 
three  minor  chords,  with  the  octave  of  the  various  tones. 

(a)  The  method  of  building  up  the  major  diatonic  scale  is  as  fol- 
lows :  Assign  to  Cs,  as  the  first  of  three  tones  with  vibration-num- 
bers as  4:5:6,  any  number  of  vibrations,  as  256  per  second.  Its 
octave  will  have  512  vibrations;  and  the  tones  of  the  major  chord 
will  have  respectively  256  x  f  ,  256  x  f  ,  256  x  f  ,  vibrations  per  second. 
Designating  these  four  tones  by  their  absolute  names,  we  have  :  — 

C3        Z>3        Es        Fs         G3        A3        B3         C4 
256         ?         320         ?         384         ?  ?         512. 

Taking  Ct  as  the  third  tone  of  another  major  chord,  we  have  :  — 
4:5:6  =  ?:?:  512  =  341£  :  426|  :  512. 


Assigning  the  two  vibration-numbers  thus  found  to  Fs  and  As,  we 
have  :  — 

Cs        Z>3        Es        F3         Gs        A  3        £3         C4 
256         ?         320      341|      384      426f        ?         512. 

Again,  starting  with  Gz  =  384,  as  the  first  tone  of  another  major 
chord,  we  have  the  series  :  — 

4  :  5  :  6  =  384  :  ?  :  ?  =  384  :  480  :  576  . 

The  tone  with  480  vibrations  will  be  called  Bs,  as  it  lies  between  ;, 
those  already  called  A3  and  C±.     The  last  tone,  having  576  vibrations,  ' 
must  be  placed  beyond   C*4,  but  the  tone  an  octave  lower,  with  a 
vibration-number  half  as  great,  288,  falls  between  C$  and  Es.     This 
lower  tone  we  will  call  Ds. 


CHARACTERISTICS   OF   TONES.  233 

The  three  chords  and  the  complete  series  formed  from  them,  in 
musical  notation,  with  their  respective  vibration-numbers,  which  will 
be  found  to  be  in  the  ratios  already  given,  are:  — 


s 


C3      D3      E3      F3      G3     A3      B3      C4 
256    288    320  341.3  384  426.6  480    512 


(6)  A  minor  diatonic  scale  may  be  constructed  from  three  minor 
chords,  founded  upon  any  assigned  pitch,  in  the  same  manner  as 
described  above  for  the  major  scale. 

198.  Chromatic  Scale.  —  In  music,  other  tones  of  the 
simple  scale  already  described  are  needed  as  the  beginnings 
of  similar  diatonic  scales.  For  instance,  D3  may  be  used 
as  the  keynote.  With  this,  three  chords  may  be  formed, 
using  the  intervals  4  :  5  :  6,  as  follows  :  — 

4  :  5  :  6  =  288  :  380  :  432 
4  :  5  :  6  =  384  :  480  :  576 
4:5:6  =  432:540:2  x  324. 

The  new  complete  series  is  :  — 

A     i      <>     a*     <>     B,     <>     D4 

288     324     380     384    432     480    ,540     576. 

Thus  four  new  tones  are  introduced  by  using  D3  as  the 
keynote.  Any  other  tone  of  the  first  scale,  or  any  of 
these  new  tones,  may  be  used  as  new  keynotes.  If  we 
form  the  twenty-four  scales  ordinarily  used  in  music, 
twelve  major  and  twelve  minor,  no  fewer  than  seventy- 
two  tones,  within  the  limits  of  the  octave,  will  represent 
them.  To  use  so  many  tones  in  each  octave  of  keyed 
instruments,  such  as  the  piano  and  organ,  is  a  practical 


234  SCHOOL  PHYSICS. 

impossibility.  As  many  of  these  tones  differ  from  each 
other  but  little,  musicians  have  agreed  to  make  a  com- 
promise by  giving  up  the  simple  perfection  of  the  inter- 
vals of  the  chords  described,  and  to  divide  the  octave  into 
twelve  equal  intervals,  called  semi-tones.  The  series  of 
thirteen  semi-tones,  separated  by  the  twelve  equal  intervals, 
constitutes  the  modern  chromatic  scale. 

(a)  The  eight  tones  nearest  those  already  described  are  named  as 
we  have  already  designated  them,  while  the  five  interpolated  tones, 
corresponding  to  the  black  keys  on  the  piano  keyboard,  are  called 
sharps  of  the  tones  immediately  below  them  or  flats  of  the  tones  next 
above  them.  The  compromising  process  between  theory  and  practice, 
or  the  principle  by  which  the  octave  is  divided  into  twelve  equal 
intervals,  is  called  equal  temperament.  In  this  system,  the  only  perfect 
interval  is  the  octave,  and  all  chords  are  slightly  "  out  of  tune." 

(6)  The  interval  in  this  scale  is  ^/o  =  1.05946.  Any  tone  being 
given,  the  next  above  is  found  by  multiplying  by  1.05946,  or  the  next 
below  by  dividing  by  the  same  number.  The  equal  tempered  chro- 
matic scale  founded  upon  the  international  pitch,  A3  =  435  vibrations, 
as  universally  used  in  music,  is  as  follows  :  — 


n  u.         G    &    J 


C3      C33    D3    D3S    E3    F3    F33    G3    G3S    A3    A3S    B3    C4 

258.6     274.0   290.3  307.5  325.8  345.2  365.8  387.5  410.6    435    460.9  488.3  517.3 


Tones  and  Overtones. 

Experiment  125.  —  Repeat,  Experiment  114,  using  the  soft  cotton 
rope  or  the  long  wire  spiral  used  in  Experiment  115.  By  properly 
timing  the  motion  of  the  hand,  the  rope  may  be  made  to  vibrate  as 
a  whole.  Doubling  the  rapidity  of  motion  of  the  hand,  the  rope  or 
spiral  divides  itself  into  two  vibrating  segments,  separated  from  each 
other  by  a  point  of  apparent  rest  called  a  "node."  Trebling  or 
quadrupling  the  rapidity  of  the  motion  of  the  hand  causes  the  rope 
or  spiral  to  divide  into  three  or  four  segments  separated  by  a  corre- 
sponding number  of  nodes.  In  each  case,  the  period  of  the  hand 


UNIVERSITY  OF  CALfFORWA 

DEPARTMENT  OF  PHYSICS 
CHARACTERISTICS  OF  TONES.  235 

must  synchronize  with  that  of  the  rope  or  spiral  and  of  the  several 
segments,  but  by  a  little  practice  one  may  so  time  the  motions  of  the 
hand  as  to  bring  out  the  segmental  vibrations  just  described. 

Experiment  126.  —  Bow  or  pluck  the  string  of   a  sonometer  (see 
Fig.  171)  near  its  end,  thus  setting  it  in  vibration  as  a  whole.     The 


FIG.  169. 

string  will  have  the   appearance   of  a  single  spindle  as  shown  in 
Fig.  169,  and  will  sound  the  lowest  tone  that  it  is  capable  of  produc- 


FIG.  170. 

ing.     Lightly  touch  the  wire  at  its  middle  point  with  the  tip  of  the 
finger  or  the  beard  of  a  quill;  the  wire  will  vibrate  in  halves  (Fig.  170) 


FIG.  171. 


and  sound  a  tone  an  octave  above  that  previously  heard.     Sound  the 
sonometer  again,  touch  the  string  as  before,  and  try  to  distinguish 


236  SCHOOL   PHYSICS. 

both  tones  as  coming  simultaneously  from  the  apparatus.  Again  set 
the  string  in  vibration  and  touch  it  at  one-third  its  length.  The 

vibrating     string    di- 
vides  into    thirds    as 
shown    in     Fig.    171, 
v      n  and  emits  a  tone  that 

==H*==  =-B     the  trained  ear  recog- 

FlG  172  nizes   as    the   fifth  of 

the  octave  above  that 

first  sounded.  Probably  both  sounds  will  be  heard  at  the  same  time. 
In  similar  manner,  a  string  sufficiently  long  may  be  made  to  vibrate 
in  any  aliquot  part  of  its  whole,  as  fourths,  fifths,  ninths,  tenths,  etc. 
The  string  should  be  touched  at  n  and  bowed  at  v,  as  shown  in 
Fig.  172. 

199.  Fundamental  Tones  and  Overtones.  —  The  tone  that 
is  sounded  by  a  body  vibrating  as  a  whole,  i.e.,  the  lowest 
tone  that  such  a  body  can  produce,  is  called  its  fundamental 
or  primary  tone.     The  tones  produced  by  the  vibrating  seg- 
ments of  sonorous  bodies  are  called  overtones,  partial  tones, 
or  harmonics.     The  partial  tones  are  named  first,  second, 
third,  etc.,  in  the  order  of  their  vibration-numbers,  begin- 
ning with  the  fundamental. 

(a)  It  is  customary  to  regard  both  ends  of  the  string  as  nodes. 
The  points  of  greatest  vibration,  midway  between  the   nodes,  are 
called  anti-nodes.     If  little  A-shaped  riders,  made  of  slips  of  paper 
bent  in  the  middle,  are  placed  on  a  string  and  the  string  is  then 
made  to  vibrate  in  segments,  the  riders  at  the  nodes  will  remain  in 
position  while  those  at  the  anti-nodes  will  be  thrown  off  as  shown 
in  Fig.  171. 

(b)  The  interval  from  the  fundamental  to  the  first  overtone  is  an 
octave ;  to  the  second,  an  octave  and  a  fifth;  to  the  third,  two  octaves; 
to  the  fourth,  two  octaves  and  a  major  third  ;  to  the  fifth,  two  octaves 
and  a  fifth,  etc. 

200.  Quality  or  Timbre  is  the  characteristic  by  which 
we  distinguish  one  tone  from  another  of  the  same  intensity 


CHARACTERISTICS   OF  TONES.  237 

and  pitch.  The  middle  C  of  a  piano  is  essentially  different 
from  the  same  tone  of  an  organ,  and  any  tone  of  a  flute  is 
distinguishable  from  any  tone  of  a  violin.  The  physical 
basis  of  quality  is  wave-form,  and  is  due  to  the  number, 
relative  intensities,  and  relative  phases  of  the  overtones 
that  accompany  the  fundamental. 

(a)  The  well-trained  ear  can  detect  several  tones  when  a  piano- 
key  is  struck.  In  other  words,  the  sound  of  a  vibrating  piano-wire 
is  a  compound  tone  (see  Experiment  138) .  The  sound  of  a  tuning- 
fork  is  a  fairly  good  example  of  a  simple  sound.  By  sounding  simul- 
taneously the  necessary  number  of  forks,  each  of  proper  pitch  and 
with  appropriate  relative  intensity,  Helmholtz  showed  that  the  com- 
pound sounds  of  musical  instruments,  including  even  the  most 
wonderful  one  of  all,  the  human  voice,  may  be  produced  synthetic- 
ally. Simple  tones  lack  the  richness  that  is  so  highly  prized  in 
musical  instruments. 

(6)  The  way  in  which  a  single  string  can  simultaneously  give  rise 
to  several  tones,  i.e.,  how  the  segmental  vibrations  are  imposed  upon 
the  fundamental,  may 
be    explained    as  fol- 
lows :  In  Fig.  173,  AB    A^^ 
represents     a      string  Fio.  173. 

which,  when  vibrating 
as  a  whole,  sounds  its  fundamental,  and  assumes  the  form  A  CB. 

Fig.  17-i  represents  the  same  string  sounding  its  fundamental  and 
its  first  overtone.  In  this  case  the  fundamental  is  represented  by 

the  dotted  line,  while 

-£U^ _  the     resultant      com- 

^        ""^>>g    pound    tone   is   repre- 
F      m  sented  by  the  continu- 

ous line,  *A  CB.    While 

AB  vibrates  as  a  whole,  its  halves,  AC  and  CB,  vibrate  in  opposite 
directions,  and  with  doubled  rapidity. 

Fig.  175  represents  the  compounding  of   the  same  fundamental 
with   its   second    over- 
tone. The  fundamental 
is  represented    by  the 
dotted  line   as   before,  FlG-  175- 


288  SCHOOL  PHYSICS. 

while  the  resultant  compound  tone  is  represented  by  the  continuous 
line,  ADD'B.  While  A B  vibrates  as  a  whole,  its  thirds,  AD,  DD', 
and  D'J3,  vibrate  in  alternately  opposite  directions,  and  with  trebled 
rapidity.  The  difference  in  the  three  wave-forms  is  manifest  in  the 
figures.  Such  combinations  may  be  made  in  almost  endless  variety, 
each  combination  representing  a  compound  tone  that  varies  from  all 
of  the  others. 

201.  The  Graphic  Method  of  studying  sounds,  which 
fairly  meets  even  the  exacting  demands  of  physicists,  and 

is  largely  used  by  them, 
may  be  briefly  explained 
thus:  Suppose  the 
smoked  plate  of  Fig.  150 
to  be  a  sheet  of  smoked 
paper  fastened  upon  the 
surface  of  a  cylinder  that 
is  so  mounted  that,  when 
it  is  turned  by  a  crank, 
the  screw  cut  upon  the 

FIG.  176.  .  ,,  ,.     , 

axis  moves  the  cylinder 

endwise,  as  shown  in  Fig.  176.  Such  an  instrument  is 
called  a  vibroscope. 

(a)  When  the  style  *of  a  vibrating  tuning-fork  just  touches  the 
paper,  and  the  crank  is  turned,  the  vibrations  will  be  traced  in  the 
form  of  a  sinusoidal  spiral  upon  the  smoked  surface,  the  amplitude, 
length  and  form  of  each  wave  being  truthfully  recorded.  The  cylin- 
der may  be  turned  by  clockwork.  By  counting  the  number  of  waves 
traced  in  one  second,  we  obtain  directly  the  vibration-number  of  the 
fork.  By  various  ingenious  and  delicate  devices,  the  wave-forms  that 
correspond  even  to  a  very  complex  tone  may  thus  be  secured  for  study 
or  illustration.  Such  a  record  may  be  written  parallel  with  that  of  a 
tuning-fork  of  known  frequency  (i.e.,  vibration-number),  and  com- 
parative study  thus  facilitated.  For  instance,  if  the  record  of  a 
phonautograph  (see  dictionary)  shows  that  while  the  fork  recorded 


CHARACTERISTICS   OF  TONES.  239 

70  vibrations,  a  singing  voice  recorded  180,  and  the  vibration-number 
of  the  fork  is  known  to  be  100,  a  simple  proportion  (70 : 180  : :  100 :  x) 
shows  that  the  vibration-number  of  the  voice  was  257i,  indicating 


FIG.  177. 


a  tone  almost  identical  with  that  of  middle  C  of  the  pianoforte. 
Fig.  177  shows  traces  of  several  compound  tones,  each  written  below 
the  sinusoidal  tracing  of  the  tuning-fork. 


Manometric  Flames. 

Experiment  127.  —  From  an  inch  board,  cut  a  strip,  A,  2  inches 
wide  and  10  inches  long.  Cut  another  block,  B,  2  inches  square. 
Placing  the  point  of  an  inch  center-bit  an  inch  from  the  end  of  A, 
bore  a  shallow  hole,  about  |-  of  an  inch  deep,  in  one  side  of  the 
strip.  Bore  a  similar  hole  at  the  middle  of  one  side  of  B.  Place 
the  point  of  a  |-inch  center-bit  at  the  center  of  the  shallow  hole 
in  A,  and  bore  a  hole  through  the  wood.  Bore  two  T3g-inch  holes 
from  the  bottom  of  the  shallow  hole  in  B  and  through  the  wood,  one 
directly  through  the  block  at  the  center,  and  the  other  obliquely 
downward  from  the  lower  edge  of  the  hole.  Stretch  a  piece  of  gold- 
beater's skin,  or  of  the  thinnest  sheet  rubber  you  can  find  (toy  balloon) 
over  the  mouth  of  the  shallow  hole  in  B,  gluing  it  there.  Spread 
glue  over  the  face  of  A  around  the  shallow  hole  and  screw  A  and  B 
together,  so  that  the  two  shallow  holes  shall  come  face  to  face  with 
the  elastic  membrane  between  them.  The  "  manometric  capsule  "  is 
complete.  Xail  the  other  end  of  .4  to  a  base  board,  as  shown  in 
Fig.  178.  Set  a  glass  tube,  e,  into  the  i-inch  hole  of  A,  making  the 
joint  tight  with  a  strip  of  paper  smeared  with  glue  and  wrapped 
about  the  end  of  e  before  it  is  forced  into  the  hole.  Attach  one  end 
of  a  piece  of  large-sized  rubber  tubing  to  the  glass  tube,  6,  and  the 
other  end  to  a  trumpet  made  by  rolling  up  a  piece  of  cardboard  into 


240 


SCHOOL  PHYSICS. 


a  cone  about  8  inches  long  and  2  inches  across  the  mouth.  Into  the 
T3g-inch  hole  at  the  middle  of  B,  tightly  fit  a  glass  tube,  bent  and 
drawn  to  a  jet  at  the  outer  end.  Into  the  other  T3g-inch  hole  of  B, 
tightly  fit  a  straight  glass  tube,  c,  that  may  be  connected  with  the 
house  supply  of  illuminating  gas.  Turn  on  the  gas  and  light  it  at 
the  jet.  If  the  air  of  the  room  is  still,  the  flame  will  be  compara- 
tively steady.  Hold  a  vibrating  tuning-fork  at  the  mouth  of  the 
trumpet,  and  notice  the  flickering  of  the  flame.  This  flickering  of 
the  flame  is  the  thing  that  we  are  to  study,  and  its  cause  ought  to  be 
clearly  apparent  to  the  pupil. 

From  a  board  £  of  an  inch  thick,  4  inches  wide,  and  a  foot  long,  cut 
a  square  piece  marked  M,  and  the  twro  attached  spindles,  H  and  K. 

Taper  the  spindles  so  that 
the  whole  piece  may  be 
easily  twirled,  as  shown  in 
the  figure.  The  blunt 
point  of  the  shorter  spin- 
dle should  rest  in  a  shal- 
low pit,  on  a  firm  support. 
To  the  opposite  sides  of  M, 
fasten,  with  tacks  at  the 
lower  edge  and  with  thread 


wound  along  the  top  and 
bottom  borders,  two  pieces 
of  thin  silvered  glass,  thus 
completing  the  "revolving 
mirror."  The  support  of 
the  mirror  should  be  at 
su,ch  a  height  that  the 
flame  may  be  seen  reflected 
from  the  middle  of  the 
mirror. 

Rotate  the  mirror  and  notice  that  the  steady  flame  appears  as  a 
luminous  ribbon  of  uniform  width.  If  the  flame  is  agitated  by  the 
wind  from  the  mirror,  shield  the  flame  with  a  lamp  chimney.  While 
twirling  the  mirror,  sing  into  the  mouth  of  the  cone,  and  notice  that 
the  image  becomes  indentated,  each  tongue  indicating  an  increase  of 
pressure  on  the  diaphragm  of  the  capsule.  Each  projection  of  the 
image  corresponds  to  the  condensation  of  a  sound  wave,  and  each 
depression  to  the  rarefaction. 


FIG.  178. 


CHARACTERISTICS   OF  TONES. 


241 


FIG.  179. 


FIG.  180. 


The  vibration  of  the  flame  may  be  seen  without  using  the  mirror, 
by  quickly  turning  the  head  from  side  to  side  while  looking  at  the 
flame,  —  an  interesting  experiment. 

Experiment  128.  —  While  the  mirror  is  rotating,  sound  a  tuning- 
fork  at  the  mouth  of  the 
trumpet,  and  notice  that  the 
image  resembles  Fig.  179. 
Then  sound  a  tuning-fork 
that  is  an  octave  higher  and 
notice  that  the  image  resem- 
bles Fig.  180,  in  which  twice  as  many  tongues  as  before  are  crowded 
into  the  same  space. 

Experiment  129.  —  Remove  the  large  rubber  tubing  and  connect  e 

with  two  trumpets,  using  a 
T-pipe  or  a  Y-tube.  Sound 
the  two  forks  just  used,  and 
hold  each  at  the  mouth  of  a 
trumpet,  so  that  their  respec- 
tive waves  may  be  blended 
before  they  reach  the  diaphragm  of  the  capsule.  The  image  will  re- 
semble that  shown  in  Fig.  181.  Evidently  this  figure  could  not  have 
been  made  by  a  simple  vi- 
bration. The  alternate  con- 
densations sent  out  by  the 
fork  of  higher  piteh  unite 
with  the  condensations  sent 
out  by  the  fork  of  lower 
pitch,  thus  making  the  flame  jump  higher  by  their  combined  action 
on  the  diaphragm. 

NOTE.  —  By  singing  different  vowels  to  different  tones,  many  dif- 
ferent images  may  be  produced  in  the  rotating  mirror. 

202.  The  Optical  Method  of  studying  sounds  is  well 
illustrated  by  Mayer's  adaptation  of  Koenig's  manometric 
flames,  as  employed  in  Experiment  127.  This  method, 
like  the  graphic,  has  the  advantage  of  being  independent 

of  the  sense  of  hearing.     When  the   "manometric  cap- 
16 


FIG.  181. 


242  SCHOOL   PHYSICS. 

sule "  is  connected  by  the  tube,  e,  with  a  Helmholtz 
resonator  (§  205,  <#,),  the  flame  will  respond  to  the  tone  that 
affects  the  resonator.  By  using  a  series  of  such  resona- 
tors in  connection  with  the  flame  and  mirror,  the  analysis 
of  compound  tones  is  made  possible  even  for  one  who  is 
deaf. 

CLASSROOM  EXERCISES. 

1.  If  a  musical  sound  is  due  to  144  vibrations,  to  how  many  vibra- 
tions will  its  third,  fifth,  and  octave,  respectively,  be  due  ? 

2.  If  a  tone  is  produced  by  264  vibrations  per  second,  what  number 
will  represent  the  vibrations  of  the  tone  a  fifth  above  its  octave  ? 

Ans.  792. 

3.  A  given  tone  is  found  to  be  in  unison  with  the  tone  emitted  by 
the  inner  row  of  holes  of  the  siren  described  in  Experiment  124  when 
the  disk  is  turned  at  the  uniform  rate  of  640  times  in  30  seconds. 
Assigning  256  vibrations  for  middle  C,  name  the  given  tone. 

4.  The  vibrations  of  two  tuning-forks  are  simultaneously  recorded 
by  avibroscope.     Comparison  shows  that  9  waves  of  one  occupy  the 
same  space  as  15  waves  of  the  other.     If  the  fork  of  lower  tone  is 
marked  D,  what  should  the  other  fork  be  marked? 

5.  Determine  the  vibration-number  for  each  tone  of  a  gamut  the 
keynote  of  which  has  261  vibrations. 

6.  Is  there  any  difference  in  the  pitch  of  a  locomotive  whistle  when 
the  locomotive  is  standing  still,  when  it  is  rapidly  approaching  the 
observer,  and  when  it  is  rapidly  moving  from  him?    If  so,  describe 
and  explain  it. 

7.  What  is  the  vibration-number  of  the  tone  G  next  preceding  that 
of  a  "  violin- J.  "  fork  of  440  vibrations  ? 

8.  Why  does  the  sound  of  a  circular  saw  cutting  through  a  board 
fall  in  pitch  as  the  saw  enters  the  board? 

9.  If  an  observer  should  approach  a  sounding  organ-pipe  with  the 
velocity  of  sound,  what  would  be  the  effect  upon  the  pitch  of  the 
tone  ? 

10.  If  an  observer  should  recede  from  the  source  of  a  musical 
tone  with  a  velocity  a  little  less  than  that  of  sound,  what  would 
be  the  effect  upon  the  pitch  of  the  tone? 

11.  Suppose  that  when  an   orchestra  has   nearly  finished  a  per- 


CHARACTERISTICS   OF  TONES.  243 

formance,  an  observer  should  move  away  from  the  orchestra  with  a 
velocity  twice  that  of  sound.  Describe  his  relation  to  the  sounds 
previously  executed  by  the  orchestra. 

12.  A  tube  about  6  feet  long  is  mounted  at  its  middle  on  an  axis 
that  is  perpendicular  to  the  length  of  the  tube.  A  reed  is  fixed  at 
one  end  of  the  tube  and  may  be  sounded  by  air  forced  into  the  tube 
through  an  aperture  at  its  axis  of  rotation.  The  tube  is  sounded 
while  in  rotation.  An  observer  standing  in  a  prolongation  of  the 
axis  of  rotation  hears  a  tone  of  constant  pitch.  An  observer  standing 
in  the  plane  of  rotation  hears  a  tone  of  varying  pitch.  Explain  the 
difference. 

LABORATORY  EXERCISES. 
Additional  Apparatus,  etc.  —  Cardboard  ;  punch. 

1.  Using  the  graphic  method,  show  that  the  two  prongs  of  a  tuning- 
fork  are  moving  in  opposite  directions  at  any  given  instant. 

2.  Make  another  disk  for  the  siren  used  in  Experiment  124,  making 
eight  circles  of  holes,  each  circle  having  in  order  the  number  of  holes 
indicated  by  the  relative  vibration-numbers  given  in  §  196.     Put  this 
disk  upon  the  whirling  table  and  rotate  it  at  such  a  uniform  speed 
that  the  puffs  made  by  the  inner  circle  of  twenty-four  holes  shall  give 
a  smooth  musical  tone.     Move  the  nozzle  of  the  tube  through  which 
you  blow  over  the  several  circles  in  succession  and  name  the  familiar 
series  of  tones  that  you  hear. 

3.  Figure  182  represents  two  sets  of  sound  waves  with  like  periods 
and  phases  but  dif- 
ferent     amplitudes. 

Draw  a  single  curve 

to  represent  the  re- 

sultant    of   the    two 

series,  remembering  to  make  the  ordinates  of  the  resultant  equal  to 

the  algebraic  sum  of  the  corresponding  ordinates  of  the  constituents. 

4.  Figure  183  represents  two  such  wave  systems  meeting  in  opposite 

phases.  Draw  the 
resultant  curve  and 
tell  how  the  sound 
it  represents  corre- 
FIG.  183.  sponds  to  the  sound 

represented  by  the  resultant  drawn  in  Exercise  3,  and  how  it  differs. 


244  SCHOOL  PHYSICS. 

5.  Figure  184  represents  two  wave  systems  of  equal  periods  and 

amplitudes     but    of 
,B     opposite   phases. 
Draw   the   resultant 
FlG-  184-  and    describe    in    a 

single  word  the  sonorous  effect  that  it  represents. 

6.  Bow  a  sonometer-string  vigorously,  and  while  it  is  sounding 
lessen  the  tension.     Explain  the  discordant  groan-like  sound  that  is 
produced. 

7.  Arrange  apparatus  as  required  by  Exercise  4,  page  225.     To  the 
outer  end  of  one  of  the  tubes  connect,  by  a  funnel,  a  piece  of  large- 
sized  rubber  tubing  about  a  yard  long  and  thrust  the  shank  of  a  glass 
funnel  into  the  outer  end  of  the  rubber  tubing.     At  the  outer  end 
of  the  other  tube,  place  the  tube,  e,  of  the  manometric  capsule  and 
arrange  apparatus  as  described  in  Experiment  127.     Light  the  flame 
and  rotate  the  mirror.    Have  a  vibrating  tuning-fork  at  the  mouth  of 
the  glass  funnel,  and  notice,  directly  and  by  reflection,  the  agitation 
of  the  flame.    Shift  the  position  of  one  of  the  tubes  so  that  the  angles 
of  incidence  and  reflection  shall  be  unequal,  and  repeat  the  experiment. 


IV.    CO-VIBRATION. 

Experiment  130.  —  Support  a  soft  cotton  rope  several  yards  long 
between  two  fixed  supports,  as  the  opposite  sides  of  the  room,  or  the 
floor  and  the  ceiling.     With  a  ruler,  strike  the  rope  a  blow  near  one 
end  so  as  to  form  a 
crest,    as    shown    in 
Fig.  185.     Vary  the 
tension  of  the  rope  if 
necessary,   until  the 
crest  is   easily  seen. 
Notice  that  the  crest, 

c,  travels  from  A  to  B,  where  it  is  reflected  back  to  A  as  a  trough,  t. 
Strike  the  rope  from  above  and  thus  start  a  trough  which  will  be 
reflected  as  a  crest. 

Experiment  131.  —  Start  a  trough  from  A.     At  the  moment  of  its 
reflection  as  a  crest  at  B,  start  a  crest  at  A  as  shown  in  Fig.  186.    The 


CO-VIBRATION.  245 

two  crests  will  meet  near  the  middle  of  the  rope.     The  crest  at  the 

point  and  moment  of 

meeting  results   from       L<HI^x ^     "x|  A 


two   forces   acting   in 

the     same    direction ;  ^IG.  186- 

their  resultant  is  greater  than  either  of  the  components. 

Experiment  132.  —  Using  the  rope  as  previously  described,  start  a 
crest  at  A.  At  the  moment  of  its  reflection  at  B  as  a  trough,  start 

a  second  crest  at  ^4. 
The  trough  and  crest 
will  meet  near  the 
middle  of  the  rope. 

Vary  the  experiment  by  using  the  rope  as  shown  in  Fig.  155,  timing 
the  movements  of  the  hand  so  that  an  advancing  crest  shall  meet 
a  returning  trough  near  the  middle  of  the  rope.  The  rope  particles 
at  this  point,  being  thus  simultaneously  acted  upon  by  opposite 
forces,  will  remain  at  rest  or  nearly  so.  The  resultant  will  be  the 
difference  of  the  components.  Thus,  one  wave  may  be  made  to  destroy 
another  wave. 

203.  Coincident  Waves.  — Just  as,  when  one  crest  coin- 
cides with  another,  the  wave  has  an  increased  height,  and 
when  a  crest  coincides  with  a  trough,  the  wave  disappears, 
so,  when  the  condensation  of  a  sonorous  wave  coincides 
with  another  condensation,  the  actual  motions  of  the  par- 
ticles of  the  sound  medium  are  increased,  and,  when  a 
condensation  coincides  with  a  rarefaction,  said  motions  are 
reduced  or  destroyed.  Such  increased  resultant  motions 
of  the  material  particles  imply  an  increased  loudness  of 
the  sound.  Such  diminished  resultant  motions  imply  an 
enfeebled  sound  or  perhaps  silence. 

Sympathetic  Vibrations. 

Experiment  133.  — Repeat  Experiment  13,  and  vary  it  by  setting 
the  heavy  pendulum  in  motion  by  the  cumulative  action  of  well-timed 
puffs  of  air  from  the  mouth  or  from  a  hand-bellows. 


246  SCHOOL  PHYSICS. 

Experiment  134.  —  Suspend  several  pendulums  from  a  frame  as 
shown  in  Fig.  66.  Make  two  of  equal  length,  so  that  they  will  vibrate 
at  the  same  rate.  Be  sure  that  they  will  thus  vibrate.  The  other 
pendulums  are  to  be  of  different  lengths.  Set  a  in  vibration.  The 
swinging  of  a  will  produce  slight  vibrations  in  the  frame,  which  will, 
in  turn,  transmit  them  to  the  other  pendulums.  As  the  successive 
impulses  thus  imparted  by  a  keep  time  with  the  vibrations  of  &,  this 
energy  accumulates  in  b,  which  is  soon  set  in  perceptible  vibration. 
As  these  impulses  do  not  keep  time  with  the  vibrations  of  the  other 
pendulums,  there  can  be  no  such  marked  accumulation  of  energy  in 
them,  for  many  of  the  impulses  will  act  in  opposition  to  the  motions 
produced  by  previous  impulses,  and  thus  weaken  if  not  destroy  them. 

Experiment  135.  —  Tune  the  two  strings  of  a  sonometer  to  perfect 
unison.  Place  two  or  three  paper  "  riders  "  upon  one  of  the  strings, 
and  gently  bow  the  other.  The  "riders"  will  be  dismounted  from 
the  first  string,  even  if  the  vibrations  of  the  second  string  are  not 
audible.  The  vibrant  energy  was  carried  from  one  string  through 


FIG.  188. 

the  bridges  of  the  sonometer  to  the  other  string  and  there  accumu- 
lated. Change  the  tension  of  one  of  the  strings,  thus  destroying  the 
unison,  and  try  to  repeat  the  experiment.  Notice  that  the  sympa- 
thetic vibrations  are  not  produced. 

Experiment  136.  —  Place  two  mounted  tuning-forks  that  are  in  per- 
fect unison  several  feet  apart,  and  with  the  openings  of  their  resonant 
boxes  facing  each  other.  Sound  one  of  the  forks,  and  notice  its  pitch. 
After  a  second  or  two,  touch  the  prongs  to  stop  their  motion.  It  will 
be  found  that  the  second  fork  has  been  set  in  motion  and  is  giving 
forth  a  sound  of  the  same  pitch  as  that  originally  produced  by  the 


CO-VIBRATION. 


247 


first  fork.  With  wax,  fasten  a  small  weight  to  one  of  the  prongs  of 
the  second  fork.  An  attempt  to  repeat  the  experiment  will  fail. 
When  the  two  forks  are  in  uni- 
son, their  periods  are  the  same. 
The  second  and  subsequent 
pulses  sent  out  by  the  first  fork 
strike  the  second  fork,  already 
vibrating  from  the  effect  of  the 
first  pulse,  in  the  same  phase  of 
vibration,  and  thus  each  adds 
its  effect  to  that  of  all  its  pre- 
decessors. If  the  forks  are  not 
in  unison,  their  periods  will  be 
different,  and  but  few  of  the 
successive  pulses  can  strike  the 
second  fork  in  the  same  phase 


FIG.  189. 


FIG.  190. 


of  vibration  ;  the  greater  number  will  strike  it  at  the  wrong  instant. 

Experiment  137.  —  Fig.  190  represents  Mayer's  "sound-mill,"  which 
consists  of  four  small  resonators  attached  to  the  ends  of  a  small  cross. 
The  cross  is  carefully  balanced  on  a  ver- 
tical pivot.     The  resonators  are  made  of 
aluminium  (a  very  light  metal),  and  accu- 
rately  tuned  to   unison  with   a  mounted 
tuning-fork.     When   the   "sound-mill"    is 
placed  in  front  of  the  opening  of  the  res- 
onant box  of  the  fork  with  which  it  is  in 
unison,  and  that  fork  sounded,  the  four  resonators  turn  upon  their 
pivot,  —  a  veritable  acoustic  reaction  wheel. 

204.  Sympathetic  Vibrations.  —  It  has  been  shown 
repeatedly  that  the  motion  of  a  body  may  produce 
sound.  The  last  few  experiments  show  that  sound  may 
produce  motion.  The  most  important  feature  now  to 
be  noticed  is  that  the  sonorous  body  accumulates  only 
the  particular  kind  of  vibration  that  it  is  capable  of 
producing. 

(a)  By  the  aid  of  sympathetic  vibrations  we  are  able  to  analyze 
compound  tones,  as  is  shown  by  the  following  experiment :  — 


248 


SCHOOL  PHYSICS. 


Experiment  138.  —  Take  your  seat  before  the  keyboard  of  a  piano. 
Press  and  hold  down  the  key  of  "  middle  C,"  marked  1  in  Fig.  191, 
which  represents  part  of  the  keyboard.  This  will  lift  the  damper 
from  the  corresponding  piano  wire,  and  leave  it  free  to  vibrate. 
Strongly  strike  the  key  of  C2,  an  octave  below.  Hold  this  key  down 
for  a  few  seconds,  and  then  remove  the  finger.  The  damper  will  fall 
upon  the  vibrating  wire  and  bring  it  to  rest.  When  the  sound  of  C2 
has  died  away,  a  sound  of  higher  pitch  is  heard.  The  tone  corre- 
sponds to  the  wire  of  1,  which  wire  is  now  vibrating.  These  vibra- 
tions are  sympathetic  with  those  that  produced  the  first  overtones  of 
the  wire  that  was  struck.  These  vibrations  in  the  wire  of  1  prove  the 


FIG.  191. 

presence  of  the  first  overtone  in  the  vibrating  wire  of  C2.  In  similar 
manner,  successively  raise  the  dampers  from  the  wires  of  2,  3,  4,  and 
5,  striking  C2  each  time.  These  wires  will  accumulate  the  energy 
of  the  waves  that  correspond  to  the  respective  overtones  of  the  wire 
of  C2,  and  give  forth  each  its  proper  tone.  Thus  we  analyze  the 
sound  of  C2,  and  prove  that  overtones  are  blended  with  the  funda- 
mental. 

Some  of  these  tones  of  higher  pitch,  thus  produced  by  vibrations 
sympathetic  with  the  vibrations  of  the  segments  of  the  wire  of  C2, 
are  feebler  than  others.  This  shows  that  the  quality  of  a  tone 
depends  upon  the  relative  intensities  as  well  as  the  number  of  the 
overtones  that  blend  with  the  fundamental. 


Resonance. 

Experiment  139.  —  Hold  a  vibrating  tuning-fork  over  the  mouth  of 
a  cylindrical  jar  about  15  or  18  inches  deep,  and  notice  the  feebleness 
of  the  sound.  Pour  in  water,  as  shown  in  Fig.  192,  and  notice  that, 
when  the  liquid  reaches  a  certain  level,  the  sound  suddenly  becomes 


CO-VIBRATION. 


249 


much  louder.     The  water  has  shortened  the  air-column  until  it  is 

able  to  vibrate  in  unison  with  the  fork.     If  more  water  is  added,  the 

sound  will  become  weaker. 

If  a  fork  of  different  pitch 

is  used,  the  length  of  the 

resonant  air-column  will  be 

changed,  said   length   being 

about  one-fourth  the  length 

of  the  wave  produced  by  the 

fork. 


205.  Resonance.— The 

increase  of  sound  by  the 
sympathetic  vibrations  of 
a  body  other  than  that 
by  ivhich  it  was  originally 
produced  is  called  res- 
onance. The  apparatus 
used  to  produce  such  an 
effect  is  called  a  reso- 
nator. 


FIG.  192. 


(a)  Resonance  occurs  more  or  less  prominently  in  connection  with 
all  sound,  and  is  carefully  utilized  in  musical  instruments.  Sounding- 
boards  like  that  of  the  piano,  and  diaphragms  like  those  of  the  phono- 
graph and  telephone,  have  a  general  resonance  by  virtue  of  which 
they  are  sensitive  to  any  vibratory  motion  within  the  limits  of 
ordinary  audition.  The  audiphone  is  another  illustration  of  the 
same  fact.  When  the  lower  prong  of  the  tuning-fork  used  in  Experi- 
ment 139  vibrated  outward,  it  started  a  condensation  down  the  tube. 
This  condensation  and  the  succeeding  rarefaction  were  reflected 
upward  from  the  bottom  of  the  tube,  and  returned  to  unite  with 
other  waves  sent  out  by  the  prong.  When  the  air-column  was  made 
of  the  right  length,  the  reflected  waves  coincided  with  the  other  waves 
in  like  phases ;  i.e.,  condensation  with  condensation,  and  rarefaction 
with  rarefaction.  Under  different  circumstances,  the  direct  and 
reflected  waves  may  combine  in  different  phases,  and  thus  cause 
an  enfeeblement  of  the  sound. 


250 


SCHOOL  PHYSICS. 


(6)  It  is  found  by  experiment  that  the  diameter  of  the  tube  affects 
the  length  of  the  resonant  air-column,  so  that  an  arbitrary  correction 
has  to  be  made.  For  a  cylindrical  vessel,  the  experimental  column 
shortens  as  the  diameter  increases.  The  theoretical  column  equals 
the  experimental  column  increased  by  about  one-fourth  of  the 
diameter. 

(c)  Fig.  193  represents  a  Savart  bell  and  resonator.  The  length 
of  the  resonant  air-column  is  changed  by  means  of  the  movable  bot- 
tom of  the  resonator,  which 
is  to  be  adjusted  by  trial  for 
resonant  effect.  When  the 
bell  is  sounded,  and  its  tone 
is  just  audible,  the  approach 
of  the  tube  produces  a  marked 
reinforcement  of  sound. 

(c?)  Helmholtz  constructed 
a  series  of  resonators,  each 
one  of  which  responds  pow- 
erfully to  a  single  tone  of 
certain  pitch  or  wave-length.  They  are  metallic  vessels,  nearly 
spherical,  having  an  opening,  as  at  A  in  Fig.  194,  for  the  admis- 
sion of  the  sound-waves.  The  funnel-shaped  projection  at  B  has 
a  small  opening,  and  is  inserted  in  the 
outer  ear  of  the  observer.  Such  resonators 
are  largely  used  in  the  analysis  of  complex 
tones. 

Musical  tones  may  thus  be  picked  from 
sounds  that  are  commonly  reckoned  as 
noises ;  e.g.,  the  roar  of  the  tempest  or  the 
hum  of  a  busy  street,  or  even  from  an  at- 
mosphere apparently  in  silence.  pIG  194. 


FIG.  193. 


Interference. 

Experiment  140.  —  Hold  a  vibrating  tuning-fork  near  the  ear,  and 
slowly  turn  it  between  the  fingers.  During  a  single  complete  rota- 
tion, four  positions  of  full  sound  and  four  positions  of  silence  will  be 
found.  When  a  side  of  the  fork  is  parallel  to  the  ear,  the  sound 
is  plainly  audible ;  when  a  corner  of  a  prong  is  turned  toward  the 


CO- VIBRATION. 


251 


ear  the  waves  from  one  prong  destroy  the  waves    started  by  the 
other. 

Experiment  141.  —  Hold  a  vibrating  tuning-fork  at  the  mouth  of 
a  resonator,  and  slowly  turn  it  upon  its  axis.  Notice  that,  in  certain 
positions  of  the  fork, 
its  tone  is  nearly 
inaudible.  While 
the  tube  is  in  one  of 
these  positions,  slip 
a  paper  tube  over 
one  of  the  prongs, 
as  shown  in  Fig.  195, 
being  careful  not  to 
touch  it.  The  sound 
will  be  restored,  be- 
cause the  interfering 
sound  has  been  re- 
moved. When,  by 
removing  the  paper 
tube,  we  restore  the 
sound  of  the  second 
prong,  we  demon- 
strate the  almost  par- 
adoxical fact  that  sound  added  to  sound  may  produce  silence. 


FIG.  195. 


206.  Interference.  —  The  mutual  action  of  waves  upon 
one  another  so  that  the  effects  of  their  vibratory  motions 
are  increased,  diminished,  or  neutralized  is  called  inter- 
ference. Thus,  resonance  is,  properly  speaking,  a  variety 
of  interference.  But,  as  a  general  thing,  interference  sig- 
nifies the  coming  together  of  different  systems  of  tvaves  in 
different  phases,  so  that  the  vibratory  motion  of  the  resultant 
ivave  is  less  than  that  of  the  components.  In  this  sense, 
interference  of  sound  signifies  the  union  of  two  or  more 
systems  of  sound  waves  in  such  a  way  as  to  weaken  or 
destroy  the  sound. 


252 


SCHOOL  PHYSICS. 


(a)  If,  while  a  tuning-fork  is  vibrating,  a  second  fork  is  set  in 
vibration,  the  waves  from  the  second,  must  traverse  the  air  already 
vibrant  from  the  effects  of  the  first.  When  two  forks  that  have  the 
same  pitch  are  any  number  of  whole  wave-lengths  apart,  their  waves 
will  unite  in  like  phases,  and  a  reinforcement  of  sound  will  ensue,  as 


FIG.  196. 

indicated  by  Fig.  196.     When  the  forks  are  an  odd  number  of  half 
wave-lengths  apart,  their  waves  will  unite  in  opposite  phases,  and  a 


FIG.  197. 


silence,  perfect  or  partial,  will  ensue,  as  indicated  by  Fig.  197. 
ference  is  the  leading  characteristic  property  of  wave  motion. 


Inter- 


Beats. 

Experiment  142.  —  Simultaneously  sound  two  large  tuning-forks 
that  are  in  unison,  and  notice  that  the  sound  is  as  smooth  as  if  only 
one  fork  was  sounding.  Load  one  of  the  prongs  of  one  of  the  forks 
with  wax,  sound  both  forks,  and  notice  that  the  sound  is  not  smooth, 
but  that  a  series  of  palpitations  or  beats  is  easily  perceptible. 

Experiment  143.  —  In  a  quiet  room,  strike  simultaneously  one  of  the 
lower  white  keys  of  a  piano,  and  the  adjoining  black  key.  A  similar 
series  of  beats  will  be  heard. 

207.  Beats.  —  If  two  tuning-forks,  A  and  B,  vibrating 
respectively  255  and  256  times  a  second,  are  set  in  vibra- 


CO-VIBRATION.  253 

tion  at  the  same  time,  their  first  waves  will  meet  in  like 
phases,  and  the  result  will  be  an  intensity  of  sound  greater 
than  that  of  either.  After  half  a  second,  B  having  gained 
half  a  vibration  upon  A,  the  waves  will  meet  in  opposite 
phases,  and  the  sound  will  be  weakened  or  destroyed. 
At  the  end  of  the  second,  we  shall  have  another  reinforce- 
ment ;  at  the  middle  of  the  next  second,  another  interfer- 
ence. This  peculiar  pulsation  arising  from  the  successive 
reinforcement  and  interference  of  two  tones  differing  slightly 
in  pitch  is  called  a  beat.  The  number  of  beats  per  second 
equals  the  difference  of  the  two  vibration-numbers. 

(a)  In  Fig.  198,  the  high  crests  and  deep  troughs  represent,  in  the 
conventional  manner,  the  phases  where  the  two  tones  reinforce  each 

^A/VV^^^/X/XA^ 

FIG.  198. 

other,  while  the  intermediate  portions  of  the  curve  similarly  symbol- 
ize the  interference  phases. 

208.  Noise  and  Music. — A  noise  is  a  sound  so  complex 
that  the  ordinary  powers  of  the  ear  fail  to  resolve  it  into 
its  constituent  tones.  A  simple  tone  is  incapable  of 
resolution,  by  reason  of  its  simplicity.  A  combination  of 
sounds  that  may  be  easily  resolved  into  simple  tones  is  a 
musical  sound.  The  distinction  is  often  difficult.  The 
combination  of  sounds  heard  in  a  boiler-shop  is  surely 
a  noise,  while  the  sound  of  a  tuning-fork  mounted  on  a 
resonant  box  is  very  nearly  a  simple  tone. 


254  SCHOOL  PHYSICS. 


CLASSROOM  EXERCISES. 

1.  How  can  a  deaf  person  determine  whether  a  given  tone  is  simple 
or  compound  ? 

2.  If  two  tuning-forks,  vibrating  respectively  256  and  259  times 
per  second,  are  simultaneously  sounded  near  each  other,  what  phe- 
nomena will  follow  ? 

3.  A  musical  string,  known  to  vibrate  400  times  a  second,  gives  a 
certain  tone.     A  second  string,  sounded  a  moment  later,  seems  to 
give  the  same  tone.     When  sounded  together,  two  beats  per  second 
are  noticeable.     Are  the  strings  in  unison?     If  not,  what  is  the  rate 
of  vibration  of  the  second  string  ? 

4.  How  many  beats  per  second  will  be  produced  by  the  simultane- 
ous sounding  of  two  tones  having  vibration-numbers  of  297  and  308 
respectively  ? 

5.  Show  that  the  length  of  a  resonant  air-column  must  be  about  \ 
the  wave-length  of  the  tone  that  it  reinforces,  or  some  odd  multiple 
of  that  length. 

6.  The  notion  is  very  common,  but  without  foundation  in  fact,  that 
the  sound  heard  when  a  conch  shell  is  held  to  the  ear  is  a  lingering 
remnant  of  the  roar  of  the  ocean  from  which  the  shell  came.     Explain 
the  sound  that  is  thus  heard. 

7.  A  tuning-fork  produces  a  strong  resonance  when  held  over  a  jar 
15  inches  long,     (a)  Find  the  wave-length   of  the  fork.     (&)  Find 
the  wave-period.     Ignore  the  influence  of  the  diameter  of  the  jar. 

8.  A  tuning-fork  held  over  a  tall  glass  jar,  into  which  water  is 
slowly  poured,  receives  its  maximum  reinforcement  of  sound  when 
the  resonant  air-column  is  64.8  cm.  long.     Assuming  that  the  fork  is 
accurately  tuned  to  give  an  exact  number  of  vibrations  per  second, 
noting  the  fact  that  the  thermometer  records  a  temperature  of  16°  C., 
and  keeping  in  mind  the  probability  of  slight  experimental  error, 
determine  the  vibration-number  of  the  fork.  Ans.  132. 

9.  Refer  to  §  205  (6),  and  show  that,  representing  the  velocity  of 
sound  in  air  by  y,  the  length  of  the  resonant  air-column  by  I,  the 
diameter  of  the  resonant  column  by  d,  and  the  number  of  vibrations 
of  the  fork  by  n, 


10.  If  a  tube  4  cm.  in  diameter  and  50  cm.  long  responds  most 


CO-VIBRATION.  255 

loudly  to  a  certain  fork,  what  is  the  wave-length  of  the  tone  of  that 
fork? 

11.  One  of  two  tuning-forks,  each  tuned  to  512  vibrations  per 
second,  is  loaded  with  wax.  The  forks  are  simultaneously  sounded, 
and  20  distinct  beats  are  heard  in  10  seconds.  What  is  the  vibration- 
number  of  the  loaded  fork  ? 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Resonant-tube  and  two  tuning-forks, 
as  described  ;  wooden  rod ;  piano ;  music-box  and  wraps  for  the  same ; 
guitar;  glass  funnel;  "["- tubes. 

1.  In  a  manner  similar  to  that  employed  in  Exercise  1,  page  214, 
represent  two  series  of  waves.     Draw  the  second  circle  immediately 
under  the  first  and  with  equal  diameter.     Divide  the  circumference 
of  the  first  circle  into  eight,  and  that  of  the  other  into  twelve,  equal 
parts.     Use  the  same  scale  in  laying  off  the  equal  parts  on  the  axes  of 
abscissas  for  the  two  curves.     When  the  two  curves  of  sines  are  drawn, 
prolong  the  vertical  lines  downward  and  draw  a  third  axis  of  abscissas. 
Construct  a  curve  that  will  represent  the  form  of  the  wave  formed  by 
compounding  the  two  waves  represented  by  the  curves  previously 
drawn ;  i.e.,  make  each  ordinate  equal  to  the  algebraic  sum  of  the  two 
corresponding  ordinates. 

2.  Using  a  resonant  jar  and  a  tuning-fork  the  vibration-number 
of  which  is  known,  determine  the  velocity  of  sound  in  air.     (Apply 
the  formula  developed  in  the  solution  of  Exercise  9,  on  page  254.) 

3.  Stretch  a  string  horizontally  between  two  fixed  supports.     From 
this  string  suspend  two  bullet  pendulums  by  threads  about  a  meter 
long.     Swing  one  of  these  pendulums  across  the  direction  of  the  hori- 
zontal string.     Describe  and  explain  the  result  that  you  think  the 
exercise  was  intended  to  bring  to  your  notice. 

4.  Remove  the  cover  from  a  piano,  depress  the  pedal  so  as  to  lift 
the  dampers  from  all  the  wires,  hold  the  lips  near  the  wires,  and  sing 
the  vowel,  a,  with  the  sound  it  has  in  "fate,"  and  prolong  the  tone. 
Listen  for  the  sympathetic  response  of  the  piano.     Repeat  the  experi- 
ment, singing  the  same  vowel  with  the  sound  it  has  in  "  father,"  and 
then  the  vowel,  0,  with  the  sound  it  has  in  "  tone." 

5.  Fig.  199  represents  two  series  of  sound  waves  traveling  together. 
The  full  line  represents  one  series  and  the  dotted  line  another.   What 
phenomenon  would  result  from  such  a  combination  of  tones  as  is  here 


SCHOOL   PHYSICS. 


represented?  Describe  the  condition  of  affairs  as  represented  at  A, 
B  and  C  respectively.  Draw  a  single  curve  to  represent  the  resultant 
of  combining  these  two  tones. 


/ 


FIG.  199 

6.  Fig.  200  represents  two  systems  of  sound  waves  having  equal 
amplitudes  and  periods  that  are  as  1:2.  In  the  first  diagram,  the 
waves  start  together;  in  the  second,  the 
shorter  wave  is  a  quarter  of  a  wave-length 
behind;  in  the  third,  it  is  a  half  wave- 
length behind;  in  the  fourth,  it  is  three- 
fourths  of  a  wave-length  behind.  Draw 
curves  representing  the  compound  waves 
resulting  from  these  combinations,  and  re- 
peat each  form  twice,  thus  getting  four 
curves,  each  representing  a  series  of  three 
compound  waves.  Carefully  note  the  dif- 
ferences in  the  wave-forms  that  result 
from  combining  like  waves  in  different 
phases. 

7.  Construct  a  single  curve  that  shall 
represent  the  form   of  sound  waves  com- 
posed   of   the    combined    motions    of    the 
harmonics  represented  in  Fig.  201. 

8.  Get  a  glass  tube  about  f  of  an  inch  in 
FIG.  200.                    diameter   and  12   inches   long.     Into  this 


V 


T\ 


FIG.  201. 


CO-VIBRATION. 


257 


FIG.  202. 


tube  thrust  a  neatly  fitting  cork.  Move  the  cork  with  a  ramrod 
until,  by  trial,  you  have  adjusted  the  tube  for  maximum  resonance 
with  a  tuning-fork,  e.g.,  one  marked  "Philharmonic  A."  Support 
the  tube  with  its  mouth  close  to  the  disk 
of  the  siren  shown  in  Fig.  168,  and 
facing  one  of  the  circles  of  holes.  Hold 
the  nozzle  of  the  tube  on  the  other  side  of 
the  disk  and  just  opposite  the  mouth  of 
the  resonant  tube.  Turn  the  tube  with 
gradually  increasing  speed,  and  blow  air 
through  the  tube.  When  the  sound  is 
at  its  maximum,  the  siren-tone  will  be  in  unison  with  the  tone  of  the 
fork  by  which  the  resonant  tube  was  tuned.  Determine  the  vibration- 
number  of  the  fork. 

9.  Support  a  wooden  rod  about  an  inch  square  and  three  feet  long 
with  its  lower  end  resting  upon  the  cover  of  a  music-box  that  is  sound- 
ing.     Wrap  the  music-box  in  cotton-wool  and  manifold  layers  of 
woolen  cloth,  until  no  sound  from  the  box  can  be  heard.     Carefully 
balance  a  guitar  or  violin  upon  the  top  end  of  the  rod.     Describe  and 
explain  the  consequent  phenomenon. 

10.  Place   two  tuning-forks  having  frequencies   of    512  and  516 
respectively  upon  the  table,  and  sound  them  together.     They  will 
give  four  beats  per  second.     Make  sure  of  the  fact  by  trial.     Place 
your  ear  in  a  line  with  the  forks,  and  have  one  of  the  sounding  forks 
steadily  moved  toward  the  other  at  the  rate  of  two  feet  per  second. 
How  many  beats  per  second  do  you  hear?     Then  have  one  of  the 
sounding  forks  moved  directly  away  from  the  other  at  the  uniform 
rate  of  two  feet  per  second.     How  many  beats  per  second  do  you 
hear?    Explain. 

11.  With  glass  funnel  and  T-tubes  and  rubber  tubing,  arrange 
apparatus  as  shown  in  Fig.  203.     A  sound  wave  entering  at  o  will 

divide  its  energy,  part 
passing  by  way  of  a 
and  part  by   c,   and 
uniting  at  e.     If  the 
two  paths  between  b 
and    e   are    of    equal 
lengths,     the    waves 
will  unite  at  e  in  like  phases,  and  the  ear  at  s  will  hear  the  sound 
without  serious  diminution.     If,  however,  one  path  is  longer  than 
17 


FIG.  203. 


258  SCHOOL  PHYSICS. 

the  other  by  a  half  wave-length  of  the  sound  entering  at  o,  or  any 
odd  multiple  thereof,  the  waves  will  unite,  at  e  in  opposite  phases, 
and  an  interference  more  or  less  nearly  complete  will  result.  Pro- 
vide a  tuning-fork  with  a  frequency  of  about  512 ;  determine,  by 
experiment  or  computation,  the  length  of  its  waves  at  the  tempera- 
ture of  the  room,  and  make  one  branch  of  the  apparatus  a  half  wave- 
length longer  than  the  other.  This  difference  will  be  about  a  foot. 
Sound  the  fork  at  o  and  hold  the  ear  at  s,  and  slip  one  end  of  c  back 
and  forth  over  the  glass  tubing,  until  the  adjustment  is  such  that  the 
sound  heard  at  s  is  very  feeble  or  nil.  When  a  good  interference  is 
secured,  sound  the  fork  again,  and  pinch  the  rubber  tubing  at  a  or  c. 
Two  Y-tubes  may  be  used  instead  of  the  T-tubes,  and  the  tube 
between  b  and  e  may  consist  in  part  of  a  bent  glass  tube  that  will 
slide  inside  the  rubber  tube. 


V.    THE   LAWS   OF   VIBBATIOK 

209.  Vibrations  of  Strings.  —  The  laws  of  the  vibrations 
that  give  rise  to  musical  tones  are  most  conveniently 
studied  by  means  of  stringed  instruments,  especially  the 
sonometer  (Fig.  204).  The  vibrations  maybe  transverse, 


FIG.  204. 


torsional,  or  longitudinal,  as  stated  in  §  180.  Of  these, 
the  transverse  vibrations  are  the  most  important.  When 
used  for  the  production  of  musical  tones,  strings  are 


THE   LAWS   OF   VIBRATION.  259 

fastened  at  their  ends,  stretched  to  proper  tension,  and 
then  made  to  vibrate  by  bowing,  as  in  the  violin  ;  by 
plucking,  as  in  the  guitar  or  banjo  ;  or  by  striking  them 
with  a  light  hammer,  as  in  the  piano  or  dulcimer.  •  The 
manner  of  producing  the  vibrations  has  little  effect  upon 
the  tone,  which  is  chiefly  determined  by  the  length,  diame- 
ter, density,  and  tension  of  the  string  itself. 

Experiment  144.  —  Remove  the  sliding  bridge  of  the  sonometer, 
stretch  one  of  the  strings  and  pluck  or  bow  it  near  its  end.  Xotice 
the  pitch  of  the  tone.  Place  the  sliding  bridge  at  the  middle  of  the 
scale  on  the  sonometer  box  so  as  to  halve  the  length  of  the  string ; 
then  bow  as  before.  Xotice  that  the  pitch  of  the  tone  is  an  octave 
higher.  If  desirable,  the  experiment  may  be  modified  by  tuning  the 
string  until  its  tone  is  in  unison  with  a  certain  tuning-fork  or  with 
the  tone  of  the  siren  when  the  air-stream  is  directed  against  the 
inner  row  of  holes.  Then  the  tone  of  the  half  string  will  be  in 
unison  with  another  fork  an  octave  higher  in  pitch  or  with  the  siren- 
tone  when  the  air  stream  is  directed  against  the  outer  row  of  holes, 
the  speed  of  rotation  being  the  same. 

Experiment  145.  —  Stretch  two  wires  of  the  same  diameter  and 
material  with  unequal  but  known  weights,  and,  with  the  movable 
bridge,  shorten  the  wire  that  carries  the  smaller  weight  until  it  sounds 
in  unison  with  the  other.  Xotice  that  the  lengths  of  the  strings  vary 
as  the  square  roots  of  the  weights  or  tensions. 

Experiment  146.  —  Stretch  two  iron  wires  of  different  diameters, 
upon  the  sonometer,  with  equal  tension.  With  the  sliding  bridge, 
shorten  the  heavier  wire  until  it  is  in  unison  with  the  other  wire. 
From  the  scale  on  the  sonometer  box,  read  the  length  of  the  vibrating 
part  of  the  heavier  wire.  Measure  the  diameters  of  the  two  wires  and 
notice  that  the  diameters  of  the  wires  are  inversely  proportional  to 
their  lengths. 

Experiment  147.  —  Stretch,  with  equal  tension,  a  brass  and  a  steel 
wire  of  the  same  diameter,  and,  with  the  sliding  bridge,  shorten  one 
of  the  wires  until  the  two  are  in  unison.  Ascertain,  in  the  easiest 
way,  the  densities  of  brass  and  steel,  and  notice  that  the  lengths  of 


260  SCHOOL   PHYSICS. 

the  strings  vary  inversely  as  the  square  roots  of  the  densities  of  the 
materials. 

210.  Laws  of  Vibrations  of  Strings.  —  These  experi- 
ments indicate  the  following  facts  relative  to  musical 
strings  :  — 

(1)  Other  conditions  being  the  same,  the  vibration-numbers 
vary  inversely  as  the  lengths. 

(2)  Other  conditions  being  the  same,  the  vibration-numbers 
vary  directly  as  the  square  roots  of  the  tensions. 

(3)  Other  conditions  being  the  same,  the  vibration-numbers 
vary  inversely  as  the  diameters. 

(4)  Other  conditions  being  the  same,  the  vibration-numbers 
vary  inversely  as  the  square  roots  of  the  densities. 

(a)  The  third  and  fourth  laws  may  be  consolidated  as  follows :  — 
Other  conditions  being  the  same,  the  vibration-numbers  vary  inversely 

as  the  square  roots  of  the  weights  per  linear  unit. 

(&)  In  instruments  like  the  piano,  the  length,  diameter,  and  density 

of  the  strings  are  determined  once  for  all  by  the  manufacturer,  the 

tension  being  adjusted  by  the  piano  tuner. 

Air  Columns. 

Experiment  148. — Make  a  reed-pipe  by  cutting  a  piece  of  wheat 
straw  eight  inches  (20  cm.)  long  so  as  to  have  a  knot  at  one  end. 
At  r,  about  an  inch  from  the  knot,  cut  inward  about  a  quarter  of  the 
straw's  diameter ;  turn  the  knife  blade  flat  and  draw  it  toward  the 


FIG.  205. 

knot.  The  strip,  rr' ,  thus  raised  is  a  reed ;  the  straw  itself  is  a  reed- 
pipe.  When  the  reed  is  placed  in  the  mouth,  the  lips  firmly  closed 
around  the  straw  between  r  and  s  and  the  breath  driven  through  the 
apparatus,  the  reed  vibrates  and  produces  vibrations  in  the  air-col- 
umn of  the  wheaten  pipe.  Notice  the  pitch  of  the  tone  thus  produced. 
Cut  off  two  inches  from  the  end  of  the  pipe  at  s.  Blow  through  the 


THE   LAWS   OF   VIBRATION.  261 

pipe  as  before  and  notice  that  the  pitch  is  raised.     Cut  off  two  inches 
more,  sound  the  pipe,  and  notice  that  the  pitch  is  still  higher. 

211.  Vibrations  of  Air  Columns.  —  Experiments  96, 139, 
and  148  show  that  when  gases  are  confined  in  tubes  they 
may  be  made  to  vibrate  as  sonorous  bodies.  The  air- 
column  may  be  set  in  vibration  by  a  vibrating  tongue,  as 
in  the  reed-pipe  of  Experiment  148,  or  in  reed  instru- 
ments like  the  melodeon,  accordion,  clarinet,  etc.,  or  by 
the  fluttering  of  air  particles  driven  against  the  edge  of 
an  opening  in  a  tube,  as  in  the  whistle,  fife,  flute,  or 
organ-pipe.  Whatever  the  way  of  producing  the  vibra- 
tions, the  dimensions  of  the  air-column  itself  determine 
the  tone.  In  Experiment  148,  we  saw  that  the  air- 
column,  and  not  the  straw  tongue,  determined  the  pitch. 

Experiment  149.  —  Fit  a  cork  loosely  as  a  piston  into  the  end  of  a 
glass  tube  about  2  cm.  in  diameter  and  30  cm.  long.  Blow  across  the 
open  end  of  the  tube  so  as  to  produce  a  steady  tone.  It  may  be  more 
easy  to  do  this  if  you  use  a  mouthpiece  made  by  flattening  the  end 
of  a  piece  of  brass  tubing.  Xotice  the  pitch  of  the  tone  produced, 
and  measure  the  length  of  the  air-column  in  the  tube.  By  trial, 
determine  the  lengths  of  the  air-columns  that  will  give  the  tones  of 
the  gamut,  and  compare  the  relative  lengths  with  the  relative 
vibration-numbers  given  in  §  196. 

Experiment  150.  —  Provide  two  glass  tubes  of  the  same  diameter 
(about  2.5  cm.),  one  being  half  as  long  as  the  other  (e.g.,  10  cm.  and 
20  cm.).  Blow  across  the  end  of  the  longer  tube  so  as  to  produce  its 
lowest  tone  while  the  other  end  of  the  tube  is  open.  Xotice  the 
pitch.  Stop  one  end  of  the  shorter  tube  with  the  hand,  ard  blow 
across  the  open  end  so  as  to  produce  the  lowest  tone.  Xotice  that 
the  pitch  of  the  short  stopped-pipe  is  the  same  as  that  of  the  long 
open-pipe.  Of  course,  if  the  school  is  provided  with  an  assortment 
of  organ-pipes  (as  is  desirable),  it  is  better  to  use  them. 

Experiment  151.  —  Procure  an  open  organ-pipe,  at  least  one  side  of 
which  is  made  of  glass.  While  the  pipe  is  emitting  its  fundamental 


262 


SCHOOL  PHYSICS. 


tone,  lower  a  small  ring  with  a  paper  bottom,  on  which  a  little  tine 
sand  has  been  strewn,  as  shown  in  Fig.  206. 
Just  inside  the  upper  part  of  the  pipe,  the  sand 
dances  right  merrily,  its  motion  becoming  less 
energetic  as  the  ring  approaches  the  middle  of 
the  pipe.  When  the  ring  is  lowered  below  this 
point,  the  agitation  of  the  sand  steadily  in- 
creases. Vary  the  experiment  by  closing  the 
open  end  of  the  pipe  with  a  cover  or  plug  per- 
forated for  the  thread  and  moving  the  sand- 
strewn  membrane  up  and  down  as  before.  The 
only  place  where  the  sand  is  not  agitated  is  at 
the  closed  end  of  the  pipe. 


212.  Laws  of  Vibrations  of  Air-Columns. 

—  Careful  and  elaborate  tests  have  veri- 
fied what  is  suggested  by  our  rude  ex- 
periments, namely,  that  — 

(1)  The     vibration-numbers     of    air- 
columns  vary  inversely  as  their  lengths. 

(2)  The  pitch  of  a  closed-pipe  is  an 
octave  below  that  of  an  open-pipe  of  the 
same  length. 


FIG.  206. 


(a)  The  two  ends  of  an  open-pipe  sounding  its  fundamental  are 
places  of  maximum  motion,  i.e.,  the  middle  points  of  ventral  seg- 
ments ;  while  at  the  middle  of  the  pipe,  where  the  direct  and 
reflected  pulses  cross  each  other,  there  is  no  motion.  This  middle 
point  is  a  node.  The  length  of  the  air-column  is  half  the  wave- 
length. In  the  stopped-pipe  sounding  its  fundamental,  the  node  is 
at  the  end,  and  the  length  of  the  air-column  is  a  fourth  of  the  wave- 
length. 

(&)  By  increasing  the  pressure  of  the  blast  that  blows  the  pipe, 
overtones  may  be  produced.  The  change  of  nodes  and  ventral  seg- 
ments may  be  shown  by  the  sand-strewn  membrane  as  before. 

(c)  If  a  hole  is  made  in  the  side  of  a  pipe  at  a  point  occupied  by  a 
node,  the  point  is  at  once  changed  to  the  middle  of  a  ventral  seg- 


THE   LAWS  OF  VIBRATION.  263 

ment,  and  there  is  a  corresponding  change  of  pitch.     This  action  is 
familiarly  shown  in  the  fife  and  flute. 

Vibrating  Rods. 

Experiment  152.  —  Hold  a  steel  rod,  a  meter  in  length,  at  its  middle 
point,  and  rub  one  of  its  halves  with  a  piece  of  resined  leather.  The 
rod  will  emit  its  fundamental  tone.  Repeat  the  experiment  succes- 
sively with  two  other  steel  rods,  one  having  the  same  length  and  a 


FIG.  207. 

different  diameter,  the  second  rod  being  just  half  as  long.  The 
second  rod  will  give  a  tone  of  the  same  pitch  as  the  first,  while 
the  shorter  rod  will  sound  a  tone  an  octave  above. 

Experiment  153.  — That  the  rubbing  of  a  rod,  as  in  Experiment 
152,  produces  longitudinal  vibrations  in  the  rod  is  prettily  shown  by 
the  apparatus  devised  by  Koenig,  and  represented  in  Fig.  208.     A 
brass   rod,   AB,  is 
supported   by  a 
clamp   at /its   mid- 
dle   point,  c.      An 
ivory  ball    is   sus- 
pended so  as  just 
to  touch  the  end  of 

the  rod.   When  the    -'.<     [[^1  T 

rod  is  rubbed  with 
resined  leather  at 
rf,  the  vibrations  FIG.  208. 

thus  set  up  in  the 

rod  repel  the  elastic  ball  in  a  very  energetic  manner.  The  rod  may 
be  clamped  in  a  vise,  and  the  ball  suspended  in  any  convenient  way. 


264 


SCHOOL   PHYSICS. 


213.  The  Vibrations  of  Rods  may  be  transverse,  longi- 
tudinal, or  torsional.  Transverse  vibrations  are  famil- 
iarly illustrated  in  the  music-box,  jews'-harp,  xylophone, 
tuning-fork,  etc.  Longitudinal  vibrations  were  illus- 
trated in  Experiment  153.  By  clasping  a  vertical  glass 
tube  with  one  hand,  and  rubbing  the  upper  half  with  a 
wetted  cloth  held  in  the  other,  it  is  possible  to  produce 
longitudinal  vibrations  that  will  shatter  the  lower  part 
of  the  tube.  For  longitudinal  vibrations  of  rods  of  any 
given  material,  the  vibration-numbers  are  inversely  pro- 
portional to  the  lengths  of  the  rods.  Such  rods  may  also 
be  made  to  vibrate  in  segments,  and  then  the  vibration- 
numbers  are  inversely  proportional  to  the  lengths  of  the 
segments.  If  a  violin-bow  is  drawn  around  a  rod  that 
-is  clamped  at  one  end,  the  rod  will  twist  and  untwist 
with  vibrations  that  are  as  isochronous  as  those  of  a 
tuning-fork,  emitting  a  tone  a  little  lower  than  that 

produced  by  longitudinal 
vibrations  of  the  same  rod 
having  the  same  number  of 
segment al  divisions. 

Vibrating  Plates. 

Experiment  154.  —  Support,  as 
shown  in  Fig.  209,  a  glass  or 
brass  plate,  square  or  round,  and 
strew  it  evenly  with  fine  sand. 
Place  the  finger  at  any  point  on 
the  edge  of  the  plate  (e.g.,  at  the 
middle  of  one  side)  so  as  to  form 
FIG.  209.  a  node  there,  and  draw  a  violin- 

bow  at  a  point  properly  chosen 
(e.g.,  near  the  adjacent  corner).     The  sand   immediately  begins  to 


THE   LAWS   OF  VIBRATION. 


265 


dance  on  the  plate  and  arrange  itself  along  nodal  lines.  By  chang- 
ing the  nodal  points  and  bowing  properly,  other  sand-figures  may  be 
produced,  one  of  which  is  shown  in  Fig.  209. 

214.  Vibrations  of  Plates.  —  The  method  of  studying  the 
vibrations  of  plates  as  just  illustrated  is  due  to  Chladni, 
after  whom  the  plates  and  figures  are  named.  The 
arrangement  of  nodal  lines  is  determined  by  the  relative 
positions  of  the  point  that  is  bowed  and  the  point  that  is 
touched  with  the  finger.  The  figures  may  be  produced 
in  multitudinous  variety.  As  the  complexity  of  the 
figures  produced  on  a  given  plate  increases,  the  pitch  of 
the  corresponding  tone  rises,  the  same  figure  always  answer- 
ing to  the  same  tone. 

Experiment  155.  —  Draw  a  violin-bow  across  the  edge  of  a  large 
goblet  nearly  full  of  water  on 
the  surface  of  which  cork  dust 
or  powdered  sulphur  has  been 
evenly  sifted.  The,  glass  bell  will 
emit  a  musical  tone  and  the  sur- 
face of  the  water  will  disclose  the 
mode  of  the  vibration.  When 
the  bell  sounds  its  fundamental 
tone,  it  vibrates  in  four  segments, 
and  the  surface  of  the  water  tells 
the  story  by  a  record  like  that 
shown  in  Fig.  210.  A  few  vigor- 
ous strokes  of  the  bow  would  set 
up  vibrations  of  amplitude  suf- 
ficient to  break  the  bell. 


FIG.  210. 


215.  Vibrations  of  Bells.  —  Just  as  a  tuning-fork  may 
be  looked  upon  as  a  rod  bent  into  a  U-snaPei  so  a  bell  ma7 
be  considered  as  a  disk  bent  into  a  cup  shape.  Like  a 
disk,  it  sounds  its  fundamental  tone  when  vibrating  in 
four  segments,  and  the  number  of  segments  is  always  even. 


266  SCHOOL   PHYSICS. 


CLASSROOM  EXERCISES. 

1.  A  musical  string  vibrates  200  times  a  second.     State  what  takes 
place  when  the  string  is  lengthened  or  shortened  with  no  change  of 
tension,  and  what  change  takes  place  when  the  tension  is  made  more 
or  less,  the  length  remaining  the  same. 

2.  A  certain  string  vibrates  100  times  a  second,      (a)  Find  the 
vibration-number  of  a  similar  string,  twice  as  long,  stretched  by  the 
same  weight.     (6)  Of  one  that  is  half  as  long. 

3.  A  string  sounding  C3  is  18  inches  long.     Must  it  be  lengthened 
or  shortened  and  how  much  to  give  the  tone  D3  ? 

4.  A  certain  string  vibrates  100  times  per  second.     Find  the  vibra- 
tion-number of  another  string  that  is  twice  as  long,  and  weighs  four 
times  as  much  per  foot,  and  is  stretched  by  the  same  weight. 

5.  A  certain  string  sounds  the  tone  C2  when  it  is  stretched  by 
a  weight  of  four  pounds.     What  weight  must  it  carry  to  give  the 
tone  F2. 

6.  A  musical  string  five  feet  long  emits  a  tone  in  unison  with  that 
of  a  fork  that  is  known  to  vibrate  256  times  a  second.     What  will 
its  vibration-number  be  when  it  has  been  shortened  two  feet? 

7.  A  sonometer  string  is  stretched  by  a  load  of  16  pounds.    What 
load  must  be  given  to  it  so  that  it  may  sound  a  tone  an  octave  lower  ? 

8.  A  tube  open  at  both  ends  is  to  produce  a  tone  corresponding  to 
32  vibrations  per  second.     Taking  the  velocity  of  sound  as  1,120  feet, 
find  the  length  of  the  tube.    If  the  number  of  vibrations  is  4,480,  find 
the  length  of  the  tube. 

9.  Find  the  length  of  an  organ-pipe  the  waves  of  which  are  four  feet 
long,  the  pipe  being  open  at  both  ends.     Find  the  length,  the  pipe 
being  closed  at  one  end. 

10.  What  will  be  the  relative  vibration-numbers  of  two  strings  of 
the  same  length,  diameter,  and  tension,  one  being  made  of  catgut  and 
the  other  of  brass,  the  density  of  brass  being  nine  times  that  of  catgut? 

11.  If  three  organ-pipes  of  the  same  dimensions  are  filled  respec- 
tively with  gases  of  different  densities,  e.g.,  air,  hydrogen,  and  carbon 
dioxide,  would  the  several  tones  emitted  agree  or  differ  in  pitch? 
Why? 

12.  How  would  you  experimentally  determine  whether  a  vibrating 
tuning-fork  has  nodes  or  not  ? 


THE   LAWS   OF   VIBRATION.  267 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Two  spring-balances,  each  of  which  will 
carry  a  load  of  30  pounds ;  four  hard  wood  triangular  prisms,  each 
about  5  cm.  long  and  with  a  triangular  altitude  of  2.5  cm. ;  spring- 
brass  wire,  No.  24  and  No.  27 ;  a  tuning-fork  with  pitch  of  middle  C, 
and  another  an  octave  lower ;  a  glass  tube  and  a  brass  rod  as  described 
belo\v ;  mercury  cup ;  two  electromagnets ;  voltaic  cell. 

1.  Set  two  screws  horizontally  into  the  end  of  a  table-top,  and  about 
15  cm.  apart.     Anneal  the  two  ends  of  a  piece  of  No.  24  spring-brass 
wire,  about  150  cm.  long,  and  fasten  one  of  the  ends  to  one  of  the 
screws,  and  the  other  end  to  the  hook  of  one  of  the  spring-balances. 
To  the  ring  of  the  balance,  attach  a  stout,  soft  iron  wire,  about  50  cm. 
long.     Within  easy  reach  of  the  free  end  of  this  second  wire,  set  a 
stout  screw,  so  that  its  head  shall  project  about  2.5  cm.  above  the  top 
of  the  table,  and  fasten  the  free  end  of  the  wire  to  it.     In  similar 
manner,  stretch  a  No.  27  spring-brass  wire  parallel  with  the  No.  24 
wire.     Prop  the  dynamometers  so  that  they  will   He  flat   on   their 
backs,  and  slip  one  of  the  hard  wood  prisms  under  each  end  of  each 
of  the  two  brass  wires.     Put  the  No.  24  wire  under  a  tension  of  20 
pounds,  and  move  the  prism  away  from  the  dynamometer  hook  until 
the  wire,  when  plucked  midway  between  the  prisms,  gives  a  tone  that 
is  in  unison  with  the  fork  of  lower  tone.     In  doing  this,  press  the 
wire  lightly  against  the  ridge  of  the  moved  prism,  hold  the  ear  near 
the  wire  and  let  the  rough  overtones  die  away,  leaving  the  funda- 
mental which  is  to  be  tested.     Measure  the  distance  between  the  two 
ridges ;  i.e.,  the  length  of  the  vibrating  wire.     Shift  the  prism  again 
and  determine  the  length  of  the  wire  when  its  tone  is  in  unison  with 
the  fork  of  tone  an  octave  higher.     Reduce  the  tension  of  the  wire  to 
5  pounds,  and  determine  the  length  of  the  wire  when  it  is  in  unison 
with  the  fork  of  lower  tone.     Put  the  No.  27  wire  under  a  tension  of 
10  pounds,  and  determine  the  lengths  of  the  wire  when  it  is  in  unison 
with  each  of  the  forks.     Consult  the  table  of  wire  gauges  in  the 
appendix,  and  notice  that  the  area  of  cross-section  for  No.  24  wire  is 
almost  exactly  twice  that  of   No.  27  wire,  and  remember  that  the 
weight  per  linear  unit  varies  as  the  area  of  cross-section.     How  do 
your  results  correspond  to  the  laws  given  in  §  210? 

2.  Replace  the  No.  27  wire  of  Exercise  1  with  a  second  No.  24 
wire  like  the  first,  and  put  it  under  a  tension  of  6  pounds.     Increase 
the  tension  of  the  first  wire  to  24  pounds.     Move  the  bridge  until  the 


268  SCHOOL  PHYSICS. 

second  wire  gives  a  musical  tone.  Move  the  other  bridge  until 
the  other  wire  has  the  same  length.  With  the  siren,  determine  the 
vibration-numbers  of  the  two  shortened  wires,  and  see  how  the  ratios 
between  them  compare  with  the  ratios  between  the  two  tensions. 

3.  Bring  the  siren  into  unison  with  a  tuning-fork.     Turning  the 
wheel  regularly  for  10  seconds  at  the  rate  that  gives  unison,  deter- 

"mine  the   number  of    puffs    per  second,   and    thus   determine  the 
vibration-number  of  the  fork. 

4.  Close  one  end  of  a  glass  tube  about  1.5  m.  in  length  and  4  cm. 
in  internal  diameter,  with  a  stopper.     Scatter  along  the  length  of  the 
tube  a  small  quantity  of  precipitated  silica  or  cork  dust.     Fasten  a 
thin  cork  that  neatly  fits  into  the  glass  tube  to  one  end  of  a  brass 
rod  or  tube  about  2  m.  in  length  and  1  cm.  in  diameter.     Lay  the 
glass  tube  on  the  table,  and  push  the  cork  at  the  end  of  the  brass  rod 
about  50  cm.  into  it.     Clamp  the  rod  between  two  grooved  blocks  at 
its  middle  so  that  it  shall  "lie  along  the  axis  of  the  glass  tube.     Rub 
the  outer  end  of  the  rod  with  resined  leather  so  as  to  produce  a  shrill 
sound  and  to  agitate  violently  the  powder  in  the  tube.     Change  the 
length  of  the  air-column  by  moving  the  glass  tube  endwise  until 
the  powder  divides  into  segments  separated  by  clearly  marked  nodes. 
From  the  distance  between  these  nodes,  determine  the  wave-length  of 
the  sound  in  the  air.     From  the  length  of  the  rod,  determine  the 
wave-length  of  the  sound  in  brass.      From  these  results,  determine 
the  relative  velocities  of  sound  in  brass  and  in  air. 

5.  Solder  a  wire  pointer  to  the  under  side  of  a  steel  sonometer-wire 
at  its  middle.     Place  a  small  cup  of  mercury  below  the  wire  so  that 


FIG.  211. 


the  pointer  shall  just  touch  its  surface.  Cover  the  surface  of  the 
mercury  with  a  thin  layer  of  mixed  alcohol  and  glycerin  to  keep 
the  metal  surface  clean.  Place  the  end  of  an  electro-magnet,  E,  a 


THE   LAWS   OF   VIBRATION.  269 

little  above  the  wire  and  midway  between  the  pointer  and  the  end, 
and  another  electro-magnet,  M,  at  a  distance  of  several  feet.  Put  the 
apparatus  into  circuit  with  a  voltaic  cell,  as  shown  in  Fig.  211,  and 
vibrate  the  wire.  Support  a  tuning-fork  that  is  nearly  in  unison 
with  the  wire  so  that  the  face  of  one  of  its  prongs  shall  be  near  the 
end  of  M.  Adjust  the  tension  or  the  length  of  the  wire  until  the 
response  of  the  fork  shows  that  the  wire  and  the  fork  are  in  unison. 

6.  Select  two  tuning-forks  of  the  same  tone,  and,  by  means  similar 
to  those  used  in  Exercise  5,  cause  one  to  respond  to  the  other.  Notice 
the  persistence  of  the  vibrations. 


CHAPTER   IV. 

HEAT:    MOLECULAR   PHYSICS. 

I.    NATURE   OF   HEAT,   TEMPERATURE,   ETC. 

216.  Heat  is  a  form  of  energy  into  ivhich  all  other  forms 
of  energy  are  convertible.     It  consists  in  the  agitation  of  the 
molecules  of  matter,  and  is  generally  recognized  by  the  sensa- 
tion of  warmth  to  which  it  gives  rise. 

(a)  When  the  molecular  agitation  of  a  body  is  increased,  the  body 
is  heated;  when  it  is  lessened,  the  body  is  cooled.  See  §§  6  (c),  8, 
and  51. 

217.  The  Temperature  of  a  body  is  its  state  considered 
with  reference   to  its   ability  to  communicate   heat  to  other 
bodies.     When  two  bodies  are  brought  together,  there  is  a 
tendency  toward  an  equalization  of  temperature.     If  there 
is  an  actual  transfer  between  them,  the  one  that  gives  the 
greater  amount  of  heat  has  the  higher  temperature,  and  the 
one  that  receives  it  has  the  lower  temperature , 

(a)  Water  flows  from  a  point  of  high  to  one  of  low  level.  Electrifi- 
cation flows  from  a  point  of  high  to  one  of  low  potential.  Heat  flows 
from  a  point  of  high  to  one  of  low  temperature. 

(&)  An  addition  of  heat  may  increase  the  velocity  of  the  molecular 
motion  or  it  may  do  another  kind  of  work.  When  a  body  receives 
heat,  its  temperature  generally  rises,  but  sometimes  a  change  of  con- 
dition results  instead.  When  a  body  gives  up  heat,  its  temperature 
falls  or  its  physical  condition  changes. 

Experiment  156.  —  Into  one  basin  put  hot  water;  into  a  second 
basin  put  ice-cold  water ;  into  a  third  basin  put  water  at  the  tempera- 
ture of  the  room.  Put  the"  right  hand  into  the  hot  water  and  the  left 

270 


NATURE  OF  HEAT,  TEMPERATURE,  ETC. 


271 


hand  into  the  cold  water,  and  hold  them  there  for  some  time.  Trans- 
fer the  right  hand  from  the  hot  water  to  the  water  in  the  third  basin, 
and  that  water  will  seem  cold.  Transfer  the  left  hand  from  the  cold 
water  to  the  water  in  the  third  basin  ;  the  water  that  felt  cold  to  the 
right  hand  will  feel  warm  to  the  left  hand. 

218.  An  Unsafe  Standard.  —  Experiment  156  shows  that 
our  sensations  may  not  be  trusted  as  a  measure  of  tempera- 
ture. They  are  of  even  less  value  in  the  measurement  of 
heat.  A  body  feels  hot  when  it  is  imparting  heat  to  us  ; 
it  feels  cold  when  it  is  drawing  heat  from  us. 

Experiment  157.  —  Provide  a  ring  (or  a  sheet  of  tin  with  a  hole  cut 
in  it)  and  a  metal  ball  that,  at  the 
ordinary   temperature,  will  just  pass 
through  the  opening.     Heat  the  ball 
and  it  will  no  longer  pass  through. 

Experiment  158.  —  Connect,  by  a 
perforated  cork,  a  piece  of  glass  tub- 
ing about  50  cm.  long  to  a  Florence 
flask.  Put  water  that  has  been 
colored  with  red  ink  into  the  appa- 
ratus so  that  it  partly  fills  the  upright 
tube.  Mark  the  level  of  the  water 
in  the  tube  by  a  rubber  band  or  in 
some  other  convenient  way.  Im- 
merse the  flask  in  hot  water  and 
carefully  observe  the  level  of  the 
water  in  the  tube. 


FIG.  212 


219.  Expansion.  —  Experiments  157  and  158  show  that 
one  effect  of  heating  a  body  is  to  increase  its  volume. 
This  increase  is  the  immediate  result  of  the  increase  of  the 
molecular  motions  ;  the  amount  of  the  expansion  is  defi- 
nitely related  to  the  increase  of  temperature. 

220.  A  Thermometer   is   an   inst?iument  for  measuring 
temperatures.     In  its  most  common  form,  it  consists  of  a 


272 


SCHOOL  PHYSICS. 


liquid-filled  bulb  and  a  tube  of  uniform  bore,  as  illustrated 
in  Experiment  158.  The  liquid  generally  used  is  mercury 
or  alcohol.  The  upper  part  of  the  tube  is  freed  from  air 
and  hermetically  sealed.  A  scale  of  equal  parts  is  added 
for  the  measurement  of  the  rise  or  fall  of  the  liquid  in  the 
tube. 

(a)  An  air  thermometer  consists  essentially  of  a  large  glass  bulb  at 
the  upper  end  of  a  tube  of  small  but  uniform  bore,  the  lower  end  of 
which  dips  into  colored  water.  When  the  bulb  is  heated, 
some  of  the  expanded  air  escapes  in  bubbles  through  the 
liquid ;  when  the  bulb  cools,  some  of  the  liquid  rises  in 
the  tube.  Of  course,  the  tube  has  its  scale  of  equal  parts. 
Any  slight  change  of  temperature  affects  the  elastic  force 
of  the  air  in  the  bulb  and  changes  the  height  of  the  liquid 
column.  For  a  small  change  of  temperature,  the  movement 
of  the  index  is  comparatively  large;  i.e.,  the  instrument  has 
great  sensitiveness. 

(6)  The  differential  thermometer  shows  the  difference  in 
FIG  213  temperature  of  two  neighboring  places 
by  the  expansion  of  air  in  one  of  two 
bulbs  that  are  connected  by  a  bent  glass  tube  con- 
taining some  liquid  not  easily  volatile.  It  is  an 
instrument  of  simple  construction  and  great  sen- 
sitiveness. 

(c)  Mercury  freezes  at  about- 39°  C..  For 
temperatures  lower  than  -  38°  C.,  an  alcohol 
thermometer  is  generally  used.  Mercury  boils  at 
about  350°  C.  Temperatures  higher  than  300°  C. 
are  generally  measured  by  the  expansion  of  a 
metal  rod  or  by  using  an  air  thermometer  with  a 
porcelain  or  platinum  bulb.  FlG  214 

221.  Graduation  of  the  Thermometer.  —  In  every  ther- 
mometer there  are  two  fixed  points  called  the  freezing- 
point  and  the  boiling-point.  The  first  of  these  indicates 
the  temperature  of  melting  ice  ;  the  other,  the  temperature 


NATURE  OF  HEAT,  TEMPERATURE,  ETC.      273 

of  steam  as  it  escapes  from  water  boiling  under  an  atmos- 
pheric pressure  of  76  centimeters  of  mercury.  The  dis- 
tance between  the  fixed  points  is  divided  into  equal  parts 
according  to  different  arbitrary  scales. 

(a)  The  two  scales  chiefly  used  in  this  country  are  the  centigrade 
(or  Celsius)  and  Fahrenheit's.     For  these  scales,  the  fixed 
points,  determined  as  just  explained,  are  marked  as  fol-      ^4 
lows :  — 

Centigrade.         Fahrenheit. 

Freezing-point,  0°  32° 

Boiling-point,  100°  212° 

The  tube  between  these  two  points  is  divided  into  100 
equal  parts  for  the  centigrade  scale,  and  into  180  for  Fah- 
renheit's. Either  scale  may  be  extended  beyond  either  fixed 
point  as  far  as  is  desired.  The  divisions  below  zero  are* 
considered  negative  ;  e.g.,  —  10°  signifies  10  degrees  below 
zero.  The  scales  are  designated  by  their  respective  initial 
letters,  as  5°  C.,  or  41°  F.  In  the  Reaumur  scale,  which  is 
little  used  in  this  country,  the  freezing-point  is  marked 
0°  and  the  boiling-point,  80°.  Unless  otherwise  stated, 
the  thermometer  readings  given  in  this  book  are  in  cen-  FlG-  215-. 
tigrade  degrees. 

(ft)  Since  0°C.  corresponds  to  32°  F.,  and  an  interval  of  1  centi- 
grade degree  equals  an  interval  of  1.8  Fahrenheit  degrees,  we  may 
reduce  centigrade  readings  to  Fahrenheit  readings  by  multiplying  the 
number  of  centigrade  degrees  by  1.8  and  adding  32.  Similarly,  we 
may  reduce  Fahrenheit  degrees  to  centigrade  degrees  by  subtracting 
32  from  the  number  of  Fahrenheit  degrees  and  dividing  the  re- 
mainder by  1.8. 

222.  Absolute  Zero  of  Temperature.  —  The  temperature 
at  which  the  molecular  motions  constituting  heat  wholly  cease 
is  called  the  absolute  zero.  It  has  never  been  reached,  but 
theoretical  considerations  indicate  that  it  is  273°  below 
the  centigrade  zero.  (§  232,  a.)  It  is  often  convenient 
as  an  ideal  starting-point  or  standard  of  reference. 
18 


274  SCHOOL   PHYSICS. 

(a)  Temperature,  when  reckoned  from  the  absolute  zero,  is  called 
absolute  temperature.  Absolute  temperatures  are  obtained  by  add- 
ing 273  to  the  readings  of  a  centigrade  thermometer,  or  460  to  the 
readings  of  a  Fahrenheit  thermometer. 

CLASSROOM  EXERCISES. 

1.  The  difference  between  the  temperatures  of  two  bodies  is  36 
Fahrenheit  degrees.     Express  the  difference  in  centigrade  degrees. 

2.  The  difference  between  the  temperatures  of  two  bodies  is  35 
centigrade  degrees.     Express  the  difference  in  Fahrenheit  degrees. 

3.  (a)  Express  the  temperature   68°  F.   in   the   centigrade   scale. 
(6)  Express  the  temperature  20°  C.  in  the  Fahrenheit  scale. 

4.  What  is  the  corresponding  centigrade  reading  for  50°  F.  ? 

5.  How  would  it  affect  the  readings  of  the  school  thermometer 
(mercurial)  if  the  bulb  should  permanently  contract? 

6.  How  would  the  readings  of  a  mercury  thermometer  be  affected 
if  the  tube  was  gradually  enlarged  from  the  bulb  upward ;  i.e.,  if  the 
bore  of  the  tube  was  made  slightly  conical  ? 

7.  When  a  centigrade  thermometer  indicates  a  temperature  of  15°, 
what  should  be  the  reading  of  a  Reaumur  thermometer  hanging  by 
its  side  ? 

8.  Suppose  that  one  of  the  flat  faces  of  a  tin  can  was  painted  with 
a  mixture  of  lampblack  and  oil,  the  opposite  face  of  the  can  being 
left  bright ;  that  the  can  thus  prepared  was  filled  with  hot  water  and 
hung  between   the  bulbs  of  the  differential  thermometer  with  the 
painted  side  facing  one  of  the  bulbs;   and  that  the  liquid  moved 
toward  the  bulb  that  was  opposite  the  bright  face  of  the  can.    What 
inference  would  you  draw  concerning  the  effect  of  the  paint  on  the 
facility  with  which  tin  at  a  given  temperature  emits  heat? 

9.  Suppose  that  when  the  Florence  flask  used  in  Experiment  158 
was  immersed  in  hot  water,  the  level  of  the  liquid  in  the  tube  fell  a 
little  before  it  began  to  rise.     How  would  you  explain  such  an  effect? 

10.  What  effect  would  a  diminution  of  the  bore  of  a  thermometer 
tube  have  upon  the  sensitiveness  of  the  instrument  ? 

11.  What  is  in  the  upper  part  of  a  thermometer  tube? 

12.  What  relation  has  a  flow  of  heat  between  two  bodies  to  the 
relative  temperatures  of  the  two  bodies  ? 

13.  Describe  very  briefly  the  molecular  agitations  of  a  body  at  a 
temperature  of  -273°. 

14.  What  is  the  absolute  temperature  of  this  room  at  this  time? 


NATURE  OF  HEAT,  TEMPERATURE,  ETC. 


275 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  One  or  two  chemical  thermometers 
(Fig.  215)  graduated  from  0°  to  100° ;  Bunsen  burner  or  alcohol  lamp ; 
the  boiler  apparatus  described  below ;  a  tin  pail ;  ice  or  snow ;  barom- 
eter. 

1.  Hold  a  chemical  thermometer  in  the  right  hand  as  a  pen  is  gen- 
erally held,  but  with  the  bulb  uppermost.     Strike  the  right   hand 
against  the  palm  of  the  left  hand  so  as  to  separate  some  of  the  mercury 
in  the  stem  from  the  main  column.     Measure,  in  divisions  of  the 
scale  and  at  different  parts  of  the  scale,  the  length  of  the  mercury 
thus  separated  from  the  main  column  to  determine  the  accuracy  of 
the  calibration  of  the  thermometer.     Do  not  imagine  that  this  experi- 
ment gives  any  adequate  idea  of  the  tedious  painstaking  necessary  for 
such  calibration  as  is  required  for  work  of  precision. 

2.  Xearly  fill  any  convenient  metal  vessel  with  clean  ice  in  small 
pieces,  the  smaller  the  better.     For  this  and  other  experiments  with 
heat,  snow  may  be  used  instead  of  ice.     Fill  the  spaces  between  the 
lumps  of  ice  with  water,  and  insert  the  lower  end  of  a  thermometer 
until  the  zero  mark  is  within  1  or  2  mm.  of  the  water  surface.     Place 
the  eye  so  that  the  line  of  vision  cuts  the  thermometer  at  right  angles 
at  the  top  of  the  mercury  column.     When  the  mercury  has  fallen  to 
its  lowest  point,  record  the  reading  of  the  thermometer,  estimating 
fractions  of  the  divisions  of  the  scale  with  the  eye  as  closely  as  possible. 

3.  Make,  of  sheet-copper,  a  boiler  with  a  diameter  of  10  cm.  and  a 
height  of  15  cm.     The  top  of  the  cylinder  should 

not  be  wired,  but  should  be  left  flexible.  About 
2  cm.  from  the  top,  insert  a  sheet-copper  tube,  «, 
about  5  cm.  long  and  about  6  mm.  in  diameter,  so 
that  it  shall  slope  slightly  upward  from  the  boiler. 
Provide  three  reliable  legs,  ^r  other  means  of  sup- 
porting the  boiler  about  20  cm.  above  the  table. 
Make  a  sheet-copper  conical  cover  that  fits  the 
top  of  the  boiler  snugly  and  internally  (as  a  tin 
pail  cover  fits),  and  that  tapers  upward  for  30  cm. 
^o  an  opening  about  2.5  cm.  in  diameter.  This 
opening  at  the  top  of  the  cover  should  be  so  con- 
structed that  it  may  be  closed  with  a  cork,  c.  About 
2  cm.  below  the  top  of  the  cover,  insert  a  tube,  6,  like 
that  inserted  in  the  boiler  proper,  but  only  2  cm. 
long. 


FIG.  216. 


276  SCHOOL  PHYSICS. 

Fill  the  boiler  with  water  to  the  depth  of  3  or  4  cm.  Cork  the 
tube,  a.  Pass  a  centigrade  thermometer  through  a  perforated  cork 
that  closes  c,  and  push  it  down  until  the  point  marked  100°  is  not 
more  than  2  or  3  mm.  above  the  cork,  unless  that  would  bring  the 
bulb  close  to  the  water.  In  that  case,  adjust  the  thermometer  so 
that  its  bulb  shall  be  about  3  cm.  above  the  water.  Boil  the  water 
(but  not  violently),  guarding  against  the  streaming  of  the  flame  up 
the  sides  of  the  boiler.  When  the  mercury  has  risen  as  far  as  it  will, 
record  the  reading  of  the  thermometer.  Note  the  reading  of  the 
barometer,  and  correct  the  reading  of  the  thermometer  by  allowing 
1°  for  each  27  mm.  that  the  barometer  column  exceeds  760  mm., 
or  falls  short  of  it.  Hold  a  wadded  handkerchief  over  the  mouth 
of  the  tube,  b,  and  note  the  effect  of  added  pressure  upon  the  boiling- 
point  of  the  water. 

Allow  the  thermometer  to  cool  in  air,  and  then  redetermine  its 
freezing-point,  as  in  Exercise  2.  If  that  point  varies  from  the  one 
previously  found,  consider  the  newly  found  point  as  the  true  one. 
Heat  the  ice  or  snow,  stirring  it  with  the  thermometer  during  lique- 
faction, and  observing  the  thermometric  reading. 

If  the  tests  of  the  thermometer  develop  an  error  of  1°  or  more  in 
the  fixed  points,  get  another  thermometer,  or  correct  subsequent  read- 
ings for  the  observed  errors.  In  the  estimation  of  such  errors,  the 
error  at  the  50°  mark  may  be  taken  as  the  mean  between  the  errors 
at  0°  and  100° ;  at  25°,  three  times  as  much  influence  should  be 
allowed  for  the  error  at  0°  as  for  that  at  100°. 


II.    THE  PRODUCTION   AND  TRANSFERENCE  OF 
HEAT,  ETC. 

223.  Sources  of  Heat.  —  The  sun  is  the  great  source  of 
thermal  energy,  but  man  is  able  to  transform  other  forms 
of  energy  into  heat. 

Experiment  159.  —  Rub  a  metal  button  on  the  floor  or  carpet.  It 
soon  becomes  uncomfortably  warm. 

Experiment  160.  —  Place  a  nail  or  coin  on  an  anvil  or  stone  and 
hammer  it  vigorously.  It  soon  becomes  too  hot  to  handle.  In  this 
way,  blacksmiths  sometimes  heat  iron  rods  to  redness. 


PRODUCTION  AND   TRANSFERENCE   OF   HEAT,   ETC.     277 


Experiment  161.  —  Hold  a  piece  of  iron  or  steel  against  a  dry  grind- 
stone or  an  emery-wheel  in  rapid  revolution.  The  shower  of  sparks 
noticeable  is  due  to  the  fact  that  the  small  particles  of  metal  torn  off 
by  the  grindstone  are  heated  to  incandescence. 

Experiment  162.  —  Half  fill  a  stout  four-ounce  bottle  with  mercury 
at  the  temperature  of  the  room.  Cork  the  bottle,  wrap  it  in  several 
thicknesses  of  paper  to  protect  it  from  the  heat  of  the  hand,  and 
shake  it  vigorously.  Remove  the  cork,  insert  the  bulb  of  the  ther- 
mometer, and  see  if  there  has  been  any  change  in  the  temperature  of 
the  mercury.  Cork  the  bottle  and  shake  it  as  before,  but  longer  and 
more  vigorously.  Take  the  temperature  of  the  mercury  again. 

Experiment  163.  —  Place  a  bit  of  tinder  in  the  cavity  at  the  end  of 
the  piston  of  the  "  fire-syringe  "  represented 
in  Fig.  217.  Put  the  piston  into  the  open 
end  of  the  cylinder  and  force  it  in,  com- 
pressing the  confined  air  as  abruptly  as 
possible.  Promptly  remove  the  piston.  The 
tinder  will  probably  be  on  fire. 

Experiment  164.  —  Cut  a  thin  slice  from 
a  stick  of  phosphorus  under  water.  Carry 
the  slice  011  the  knife-blade,  and  press  it 
between  the  folds  of  a  handkerchief  to  dry 
it.  Moving  it  again  upon  the  knife-blade, 
place  it  upon  a  brick.  Carefully  place  a 
single  crystal  of  iodine  upon  the  phosphorus. 
Some  of  the  potential  energy  of  chemical 
separation  wi^l  be  transformed  into  the 
kinetic  energy  of  heat. 

224.  Production  of  Heat.  —  The 
experiments  just  given  illustrate 
some  of  the  methods  by  which  other 
forms  of  energy  are  transformed  into 
heat.  The  ignition  of  a  common 

FIG.  217. 

friction-match    illustrates  the  trans- 
formation of  mechanical  energy  and   of   chemical  action 
into  heat.     Such  transformations  are  continually  taking 


278  SCHOOL  PHYSICS. 

place,    and   the   attention  has  only  to  be  called   to    the 
subject  that  they  may  be  recognized. 

(a)  The  fire  in  the  lamp  or  stove  or  grate  affords  familiar  illus- 
tration of  the  transformation  of  chemical  action  into  heat.  The 
heating  of  saws  and  other  tools  by  use,  and  of  carriage  or  car  axles 
when  not  properly  lubricated  ;  the  warming  of  hands  by  rubbing  them 
together ;  the  conversion  of  the  energy  of  the  electric  current  into  heat 
by  the  electric  lamp ;  the  old  process  of  striking  fire  with  flint  and 
steel,  are  a  few  of  the  many  illustrations  that  may  be  drawn  from 
common  life. 

Diffusion  of  Heat. 

Experiment  165.  — Thrust  an  iron  poker  into  the  fire.  The  end  of 
the  poker  that  is  held  in  the  hand  soon  grows  warm.  If  it  is  not  a 
familiar  fact  that  the  rod  has  been  heated  through  its  whole  length, 
and  that  there  is  a  gradual  rise  of  the  temperature  of  the  successive 
parts  from  the  end  held  in  the  hand  to  the  end  that  is  in  the  fire,  test 
the  rod  for  the  acquisition  of  such  information.  Hold  the  hand  over 
the  stove  and  it  is  warmed  by  the  ascending  current  of  heated  air. 
Hold  the  hand  in  front  of  the  stove  and,  in  some  way  that  we  shall 
understand  better  by  and  by,  it  receives  heat  from  the  fire. 

225.  Diffusion  of  Heat.  —  Heat  is  transferred  from  one 
point  to  another  in  two  ways,  conduction  and  convection. 

(a)  It  is  often  said  that  heat  is  transferred  in  a  third  way,  viz.,  by 
radiation.  A  heated  body,  like  the  sun,  may  communicate  periodic 
disturbances  to  a  medium  called  the  ether,  and  another  body,  like  the 
earth,  may  absorb  these  disturbances  and  be  heated  thereby.  The 
energy  thus  transmitted  is  often  called  radiant  heat,  although  it  is  not 
heat  at  all,  simply  radiant  energy  that  may  be  transformed  into  heat 
by  absorption  by  ordinary  matter.  This  so-called  radiant  heat  will  be 
considered  in  the  next  chapter. 

Conductivity  of  Solids. 

Experiment  166.  —  Turn  up  the  four  sides  of  a  sheet  of  writing- 
paper  and,  without  cutting  the  corners,  make  a  basin  about  2  cm. 
deep.  Half  fill  the  paper  pan  with  water  and  place  it  on  the  top  of  a 
hot  stove.  You  can  boil  the  water  without  burning  the  paper. 

Experiment  167.  —  Instead  of  the  iron  poker  of  Experiment  165, 
use  a  glass  rod  or  a  wooden  stick.  The  end  in  the  fire  may  be  melted 
or  burned  without  rendering  the  other  end  uncomfortably  warm. 


PRODUCTION   AND   TRANSFERENCE   OF   HEAT,   ETC.     279 

Experiment  168.  —  Put  a  silver  and  a  German-silver  spoon  into  the 
same  vessel  of  hot  water.  The  handle  of  the  former  will  become  hot 
much  sooner  than  that  of  the  latter. 

Experiment  169.  —  Place  a  bar  of  iron  and  a  similar  one  of  copper 
end  to  end  so  as  to  be  heated  equally  by  the  flame  of  a  lamp. 
Fasten  small  balls  (or  nails)  by  wax  to  the  under  surfaces  of  the  bars 
at  equal  distances  apart.  More  balls  will  be  melted  from  the  copper 


FIG.  'J18. 

than  from  the  iron.  Give  plenty  of  time  and  consider  the  number  of 
balls  that  are  melted  off,  and  not  the  promptness  with  which  a  ball  or 
two  may  fall  at  an  early  stage  of  the  experiment. 

Experiment  170.  —  Modify  Experiment  169,  by  providing  two  stout 
wires  of  iron  and  of  copper,  each  40  or  50  cm.  long.  Twist  them  to- 
gether for  about  10  cm.,  and  spread  the  untwisted  parts  so  as  to  form 
a  fork  with  a  twisted  handle.  Balance  this  fork  on  a  coverless  crayon 
box,  and  place  a  lamp  flame  under  the  overhanging  handle.  After 
several  minutes,  test  the  two  metals  with  similar  friction-matches  and 
ascertain  the  respective  distances  at  which  the  matches  will  be  ignited 
by  simple  contact  without  rubbing. 

226.  Conduction  is  the  mode  by  which  heat  is  transmitted 
from  points  of  high  temperature  to  points  of  low  temperature 
by  passing  from  one  particle  to  the  next  particle,  or  by  which 
it  is  transmitted  to  a  distance  by  raising  the  temperature 
of  the  intermediate  particles  without  any  sensible  motion 
of  them.  The  conduction  of  the  heat  is  very  gradual  and 
as  rapid  through  a  crooked  as  through  a  straight  bar. 

(rt)  The  power  of  conducting  heat  is  called  thermal  conductivity. 
Some  of  the  preceding  experiments  show  that  different  substances 


280 


SCHOOL  PHYSICS. 


have  different  conductivities,  although  part  of  the  differences  observed 
may  have  been  due  to  the  facts  that  equal  quantities  of  some  sub- 
stances require  unequal  additions  of  heat  for  equal  increments  of  tem- 
perature, and  that  some  substances  part  with  their  heat  by  radiation 
more  rapidly  than  others. 

(6)  Among  solids,  metals  are  the  best  conductors  both  of  heat  and 
of  electricity.  Owing  to  lack  of  continuity,  powdered  substances  have 
low  conductivities,  as  have  wood,  leather,  flannel,  and  organic  sub- 
stances generally.  The  relative  thermal  conductivities  of  some  metals 
are  as  follows  :  — 


Silver 100 

Copper 74 

Gold     53 

Brass 24 

Tin    .  15 


Iron     12 

Lead 0 

Platinum     8 

German  silver 6 

Bismuth  .  .  2 


Conductivity  of  Liquids. 

Experiment  171.  —  Fasten  a  piece  of  ice  at  the  bottom  of  an  ignition 
tube.  A  loosely  wound  coil  of  soft  wire  that  snugly  fits  the  tube 
will  hold  it  in  place.  Cover  the  ice  to  the  depth  of  several  inches  with 
water.  Hold  the  tube  obliquely  and  apply  the  flame  of  a  lamp  below 
the  upper  part  of  the  water.  The  water  there  may  be  made  to  boil 
without  melting  the  ice  below.  Instead  of  using  ice  and  water,  pack 
the  tube  full  of  moist  snow  if  you  can  get  it. 

Experiment  172.  —  Pass  the  tube  of  an  air  thermometer  or  of  an 
inverted  mercury  thermometer  through  a  cork 
in  the  neck  of  a  funnel.  Cover  the  thermom- 
eter bulb  to  the  depth  of  about  half  an  inch 
with  water.  Upon  the  water,  pour  a  little  sul- 
phuric ether  and  ignite  it.  The  thermometer 
below  will  scarcely  be  affected,  although  the 
water  above  may  be  boiling.  Stir  the  water 
and  note  the  prompt  movement  of  the  ther- 
mometer index.  To  prevent  the  downward 
conduction  of  the  heat  by  the  funnel,  the  ether 
may  be  placed  in  a  small  porcelain  cup  sup- 
ported by  a  wire  frame  so  that  its  bottom  dips 
into  the  water  directly  over  the  bulb. 


PRODUCTION   AND   TRANSFERENCE   OF   HEAT,    ETC.     281 


227.  Conductivity  of  Fluids.  —  Experiments  171  and 
172  indicate  that  water  has  a  very  low  conductivity,  a 
fact  that  applies  to  liquids  generally.  The  one  marked 
exception  to  this  rule  te  the  liquid  metal,  mercury.  The 
conductivity  of  copper  is  about  five  hundred  times  that  of 
water.  Gases  have  still  less,  if  any,  thermal  conductivity. 

Fluid  Currents  caused  by  Heat. 

Experiment  173.  —  Put  a  small  quantity  of  oak  filings  or  fine  saw- 
dust into  a  glass  vessel  of  water.  Heat  the  water  by  a  lamp  placed 
below,  and  notice  the  liquid  currents  as  indicated  by  the  motion  of. 
the  oak  particles. 

Experiment  174.  —  With  a  lamp  chimney  or  other  large  glass  tube, 
a  perforated  cork,  two  pieces  of  glass  tubing  4  and  15  inches  long 
respectively,  a  bit  of  rubber  tubing,  a  small 
lamp  or  a  candle,  and  two  coverless  crayon 
boxes,  arrange  apparatus  as  shown  in 
Fig.  220.  Partly  fill  the  apparatus  with 
water,  and  add  a  small  quantity  of  fine 
paper  raspings  or  of  a  paste  made  by  moist- 
ening some  aniline  dye  with  a  drop  of 
water.  Carefully  heat  the  tube  as  shown 
in  the  figure,  and  explain  any  observed 
movement  of  the  water. 

Experiment  175.  —  Cut  a  square  of  stiff 
writing  paper,  15  cm.  on  each  edge,  and 
draw  its  diagonals.  From  the  four  corners, 
cut  the  paper  along  the  diagonals  to  within 
1.5  cm.  of  the  middle  of  the  square. 
From  the  corners,  bring  four  alternate 
paper  tips  together  and  thrust  a  pin  through 

them  and  the  middle  of  the  square  and  into  the  end  of  a  penholder 
or  lead  pencil.  Hold  the  paper  wind-wheel  thus  made  over  a  stove 
or  metal  plate  that  is  very  hot,  the  wooden  handle  being  vertical 
and  above  the  paper.  One  of  the  components  into  which  the  force 
of  the  ascending  current  of  heated  air  is  resolved  sets  the  wheel  in. 
rotation. 


FIG.  220. 


282  SCHOOL  PHYSICS. 

228.  Convection.  —  When  a  portion  of  a  fluid  is  heated 
above  the  temperature  of  the  surrounding  portions,  it  ex- 
pands and  thus  becomes  specifically  lighter.  It  then  rises, 
while  the  cooler  and  heavier  portions  of  the  fluid  rush  in 
from  the  sides  and  descend  from  higher  points.  In  this 
way,  all  of  the  fluid  becomes  heated.  This  mode  of  trans- 
ferring heat  by  the  mechanical  motion  of  heated  fluids  is 
called  convection,  and  the  currents  thus  established  are 
called  convection  currents. 

(a)  Convection  currents  are  applied  to  the  heating  of  houses,  etc., 
by  hot-water  pipes  or  hot-air  furnaces,  and  constitute  the  basis  of  the 
most  common  forms  of  house  and  mine  ventilation,  the  draft  of 
chimneys,  etc.  The  Gulf  Stream  and  the  trade-winds  are  grand  con- 
vection currents. 

CLASSROOM  EXERCISES. 

1.  Why   are   hot    metal  utensils   commonly  handled   with   cloth 
"  holders  "  ? 

2.  Why  does  oil-cloth  on  a  cold  floor  feel  colder  to  bare  feet  than 
carpet  does,  both  being  at  the  same  temperature  ? 

3.  Is  a  good  conductor  of  heat  or  a  non-conductor  preferable  for 
keeping  a  body  warm  ?     For  keeping  it  cool  ? 

4.  Explain  the  non-conducting  character  of  hollow  walls,  double 
doors,  and  double  windows. 

5.  Why  is  water  heated  more  quickly  when  placed  over  a  fire  than 
when  placed  under  one  ? 

6.  Fur  and  clothing  of  loose  texture  enclose  much  air  in  their 
structure.     What  bearing,  if  any,' has  this  on  their  warmth? 

7.  Why  are  tin  tea-kettles  and  boilers  often  given  copper  bottoms  V 

8.  Draw  a  diagram  illustrating  the  heating  of   a  house  by  hot- 
water  pipes.     Explain  your  diagram. 

9.  Draw  a  diagram  showing  how  a  house  is  supplied  with   hot 
water  from   a  boiler  connected  with   the   kitchen   range   or  stove. 
Explain  your  diagram. 

10.  Draw  a  diagram  showing  how  a  house  is  heated  by  a  hot-air 
furnace,  representing  the  furnace,  cold-air  duct,  and  hot-air  pipes. 
Explain  your  diagram. 


EFFECTS   OF   HEAT.  283 


III.    EFFECTS   OF   HEAT. 

229.  Expansion  is  the  first  visible  effect  of  heat  upon 
bodies. 

Expansion  of  Solids. 

Experiment  176.  —  With  a  hack-saw,  cut  a  piece  from  one  side  of  a 
large  link  of  an  iron  chain,  and  force  the  ends  of  the  opened  link 
slightly  together  so  that  the  small  piece  may  be  pressed  hard  enough 
to  hold  it  in  place.  Heat  the  opposite  side  of  the  link.  The  metal 
will  expand  and  the  piece  will  fall  out  of  its  place. 

Experiment  177.  —  Grip  one  end  of  an  iron  rod  about  1  cm.  in 
diameter  and  30  cm.  long  so  that  the  rod  shall  be  horizontal.  Pass 
a  pivot  through  the  hole  near  the  end  of  the  meter  stick  used  in 
Exercise  8,  p.  126,  and  into  a  board.  The  iron  rod  should  lightly 
touch  the  vertical  edge  of  the  stick  a  little  below  the  level  of  the 
pivot.  Heat  the  iron  rod.  The  motion  of  the  lower  end  of  the 
meter  stick  indicates  that  the  rod  is  increasing  in  length. 

Experiment  178.  —  Get  a  straight,  compound  bar  consisting  of  a 
strip  of  brass  and  a  strip  of  iron,  each  2  or  3  mm.  thick,  2  cm. 
wide,  and  about  20  cm.  long, 

bound  face  to  face  with  wire,  or       tX      . . J         j         J        J        tt'j 
riveted  together  at   intervals  of 
about  2.5  cm.   Move  the  bar  back 

and  forth  in  a  hot  flame  so  that  the  two  metals  may  be  heated  in 
their  whole  length  and  equally.  As  the  bar  becomes  curved,  notice 
which  of  the  metals  has  expanded  the  more.  Cool  the  bar  to  the 
temperature  of  the  room  and  examine  its  form.  Bury  it  for  a  few 
minutes  in  a  freezing  mixture  of  ice  and  salt,  and  again  examine  its 
form. 

230.  Expansion  of  Solids.  —  Almost  without  exception, 
solids  expand  when  heated  and  contract  when  cooled,  the 
amount  of  expansion  varying  with  the  increase  of  the 
temperature  and  the  nature  of  the  substance. 

(a)  The  energy  of  the  expansion  and  contraction  of  solids  is  very 
great  and  enables  many  industrial  applications. 


284  SCHOOL   PHYSICS. 


Expansion  of  Fluids. 

Experiment  179.  —  Xearly  fill  a  Florence  flask  with  water  and  place 
it  upon  the  ring  of  a  retort  stand.  Support  a  long  straw  by  a  thread 
tied  near  one  end,  so  that  a  light  weight  hung  from  the  short  arm 
may  float  upon  the  liquid  surface  in  the  neck  of  the  flask  and  support 
the  long  arm  of  the  straw  in  a  horizontal  position.  Heat  the  water 
in  the  flask.  Its  expansion  will  be  shown  by  the  motion  of  the  long 
arm  of  the  straw. 

Experiment  180.  —  Close  by  fusion  one  end  of  each  of  three  similar 
glass  tubes,  15  or  20  cm.  long.  Put  water  into  one,  alcohol  into 
another,  and  glycerin  into  the  third,  using  equal  quantities  of  the 
liquids.  Place  the  three  tubes  in  a  vessel  of  hot  water  and  notice 
that  the  liquids  expand  unequally. 

Experiment  181.  —  Partly  fill  a  toy  balloon  with  air  and  tightly  tie 
the  opening.  Hold  the  balloon  over  a  hot  stove.  The  expanded  air 
fills  the  balloon.  (See  §  168.) 

Experiment  182.  —  Close  a  bottle  with  a  cork  through  which  passes 
a  glass  tube  of  small  bore  and  about  30  cm.  long.  Warm  the  bottle 
between  the  hands,  and  place  a  drop  of  ink  at  the  end  of  the  tube. 
As  the  air  in  the  bottle  contracts,  the  ink  will  move  down  the  tube, 
forming  a  liquid  index.  By  heating  or  cooling  the  bottle,  the  index 
may  be  made  to  move  up  or  down. 

Experiment  183.  —  To  a  Florence  flask,  fit  air-tight  a  delivery-tube 
that  terminates  under  water  as  shown  in  Fig.  22.  Heat  the  air  in 
the  flask,  and,  in  a  graduated  test-tube,  "  collect  over  water  "  the  air 
driven  from  the  flask.  Do  not  let  the  flask  cool  until  the  delivery- 
tube  has  been  removed  from  the  water. 

Experiment  184.  —  Fill  two  Florence  flasks  of  the  same  size  and 
shape,  one  with  air,  and  the  other  with  coal-gas.  Arrange  them  as 
described  in  Experiment  183,  and  immerse  them  to  the  same  depth 
in  hot  water,  collecting  separately  the  gases  driven  out  by  expansion. 
Compare  the  volume  of  the  gases  thus  collected. 

231.  Expansion  of  Fluids.  —  As  illustrated  by  the  ex- 
periments just  given,  liquids  and  gases  expand  when 
heated,  and  contract  when  cooled,  the  amount  of  expan- 


EFFECTS   OF   HEAT.  285 

sion  varying  with  the  increase  of  temperature.  In  the 
case  of  liquids,  the  amount  of  expansion  also  varies  with 
the  nature  of  the  substance.  The  rate  of  expansion  is 
practically  the  same  for  all  gases,  and  greater  than  it  i& 
for  solids  or  liquids. 

(a)  Substances  that  crystallize  on  cooling,  expand  as  they  approach 
the  temperature  of  solidification ;  i.e.,  a  given  quantity  of  matter 
occupies  more  space  when  it  has  a  crystalline  structure  than  it  does 
when  it  has  a  liquid  form.  Ice  is  a  good  example  of  such  a  sub- 
stance. 

Experiment  185.  —  Pour  recently  boiled  water  into  the  apparatus 
of  Experiment  182,  until  the  tube  is  half  full.  Pack  the  bottle  in 
a  mixture  of  salt  and  finely  broken  ice.  Observe  the  liquid  level 
in  the  tube.  The  water  contracts,  then  expands,  then  freezes  and 
expands. 

232.  Coefficient  of  Expansion.  —  The  elongation  per  unit 
of  length  -for  each  degree  that  the  temperature  is  raised 
above  0°,  is  called  the  coefficient  of  linear  expansion.  Simi- 
larly, the  increase  in  volume  per  unit  of  volume  for  a  change 
of  one  degree  of  temperature,  is  called  the  coefficient  of 
cubical  expansion.  It  is  generally  determined  by  dividing 
the  increment  of  volume  by  the  original  volume  as  above 
indicated.  It  may  be  taken  as  three  times  the  coefficient 
of  linear  expansion. 

(a)  For  solids,  the  coefficient  is  nearly  constant  for  different  tem- 
peratures. For  liquids,  the  coefficient  is  more  variable.  That  of 
mercury,  for  example,  is  regular  between  —  36°  and  100°,  but  for 
higher  temperatures  it  gradually  increases  in  value.  Water  exhibits 
the  most  remarkable  variation  from  regularity.  As  water  is  heated 
from  0°  to  4°,  it  gradually  contracts,  so  that  4°  is  the  temperature  of 
maximum  density  for  water.  As  the  temperature  is  raised  above  4°, 
the  water  expands,  slightly  at  first,  but  more  and  more  rapidly  as  it 
approaches  the  boiling  point.  For  gases  under  constant  pressure,  the 
coeflacient  is  nearly  constant,  with  a  value  of  -fa  or  0.00366.  (See 


286  SCHOOL   PHYSICS. 

§  222.)      For  solids,  the  linear  expansion  is  the  more  conveniently 
measured ;  for  fluids,  the -cubical. 

CLASSROOM  EXERCISES. 

1.  Why  do  wheelwrights  heat  the  tires  of  wheels  before  setting 
them? 

2.  The  bulging  walls  of  buildings  are  often  straightened  by  pass- 
ing iron  rods  from  one  wall  to  the  opposite  wall,  placing  nuts  at 
the  ends  of  the  rods,  heating  the  rods,  and  tightening  up  the  nuts. 
Explain. 

3.  Why  is  at  least  one  end  of  a  long  iron  bridge  generally  sup- 
ported upon  rollers  ? 

4.  Why  is  a  gallon  of  alcohol  worth  more  in  cold  than  in  warm 
weather,  the  market  price  being  the  same? 

5.  Explain  the  draft  of  a  lamp  chimney. 

6.  What  is  the  temperature  of  the  surface  water  of  a  pond  that 
is  just  about  to  freeze?    Of  the  water  at  the  bottom  of  the  pond? 

7.  A  certain  quantity  of  gas  is  measured  at  0°.     To  what  tempera- 
ture must  it  be  heated,  the  pressure  being  constant,  so  that  its  volume 
may  be  doubled  ? 

8.  A  mass  of  air  at  0°>  and  under  an  atmospheric  pressure  of  30 
inches,  measures  100  cubic  inches;   what  will  be  its  volume  at  40°, 
under  a  pressure  of  28  inches? 

Solution :  —  First  suppose  the  pressure  to  change  from  30  inches 
to  28  inches.  The  air  will  expand,  the  two  volumes  being  in  the 
ratio  of  28  to  30  (§  171).  100  cu.  in.  x  f f  =  107}  cu.  in.  Next, 
suppose  the  temperature  to  change  from  0°  to  40°.  The  expansion 
will  be  £•$•$  of  the  volume  at  0° ;  the  volume  of  the  air  at  40°  will 
be  l/^  times  its  volume  at  0°. 

107^  x  !/,%  =  122fff.  Am.  122fff  cu.  in. 

Alternate  Solution  :—  28  :  30  1 

273  :  273  +  40  j  : 

9.  At  150°,  what  will  be  the  volume  of  a  gas  that  measures  10  cu. 
cm.  at  15°? 

273  +  15  :  273  +  150  :  :  10  :  x.  Ans.  14.69  cu.  cm. 

10.  If  100  cu.  cm.  of  hydrogen  is  measured  at  100°,  what  will  be 
the  volume  of  the  gas  at  -  100°? 

273  +  100  :  273  -  100  :  :  100  :  x.  Ans.  46.37  cu.  cm. 

11.  A  liter  of  air  is  measured  at  0°  and  760  mm.     What  volume 
will  it  occupy  at  740  mm.  and  15.5°? 


EFFECTS   OF   HEAT.  287 

740-  760  +  !    ::  1,000  :*.  Ans.  1,085.34  cu.  cm. 

12.  A  rubber  balloon  that  has  an  easy  capacity  of  a  liter  contains 
900  cu.  cm.  of  oxygen  at  0°.     What  will  be  the  volume  of  the  oxygen 
when  it  is  heated  to  30°?  Ans.  998.9  cu.  cm. 

13.  A  certain  weight  of  air  measures  a  liter  at  0°.    How  much  will 
the  air  expand  on  being  heated  to  100°?  Ans.  366.3  cu.  cm. 

14.  A  gas  has  its  temperature  raised  from  15°  to  50°.    At  the  latter 
temperature,  it  measures  15  liters.    What  was  its  original  volume  ? 

Ans.  13,374.6  cu.  cm. 

15.  A  gas  measures  98  cu.  cm.  at  185°  F.    Wrhat  will  it  measure  at 
10°  C.  under  the  same  pressure?  Ans.  77.47  cu.  cm. 

16.  A   certain  quantity  of  gas  measures  155  cu.  cm.  at  10°,  and 
under  a  barometric  pressure  of  530  mm.    What  will  be  the  volume  at 
18.7°,  and  under  a  barometric  pressure  of  590  mm.  ? 

17.  A  gallon  of  air  (231  cubic  inches)  is  heated,  under  constant 
pressure,  from  0°  to  60°.     What   is   the  volume  of  the  air  at  the 
latter  temperature?  Ans.  281.77  cu.  in. 

18.  The  bulb  and  tube  of  an  air  thermometer  were  filled  with  boil- 
ing water.     The  bulb  being  placed  in  water  that  contained  ice,  the 
level  of  the  water  in  the  tube  fell  for  a  time  and  then  rose.     Explain. 
At  what  temperature  did  the  contraction  cease  and  the  expansion 
begin  ? 

Liquefaction. 

Experiment  186.  —  Place  snow  or  finely  broken  ice  and  a  thermom- 
eter in  a  vessel  of  watea  The  thermometer  will  fall  to  the  freezing- 
point,  but  no  further.  Apply  heat,  so  as  to  melt  the  ice  very  slowly, 
and  stir  the  mixture  constantly.  The  temperature  does  not  rise  until 
all  of  the  ice  is  melted,  or  it  rises  so  little  that  we  may  feel  sure  that 
there  would  be  no  rise  if  each  particle  of  water  could  be  kept  in 
contact  with  a  particle  of  ice. 

Experiment  187.  —  Put  a  little  water  into  a  beaker,  and  determine 
its  temperature.  Add  a  small  quantity  of  sodium  sulphate,  and  stir 
with  a  thermometer.  Notice  the  fall  of  temperature  during  the 
process  of  solution.  Repeat  Experiment  26. 

233.  The  Liquefaction  of  a  solid  is  effected  by  fusion  or 
by  solution.  In  either  case  heat  is  required  to  overcome 


288  SCHOOL   PHYSICS. 

the  force  of  cohesion,  and  disappears  in  the  process. 
Sometimes  the  absorption  of  heat  involved  in  the  lique- 
faction is  disguised  by  the  evolution  of  heat  due  to 
chemical  action  between  the  substances  used. 

(«)  The  action  of  freezing-mixtures,  e.g.,  one  weight  of  salt  and 
two  or  three  of  snow  or  pounded  ice,  depends  upon  the  fact  that  heat 
is  absorbed  or  disappears  in  the  solution  of  solids. 

Solidification. 

Experiment  188.  —  Place  a  thermometer  in  a  small  glass  vessel 
containing  water  at  30°,  and  a  second  thermometer  in  a  large  bath  of 
mercury  at  —  10°.  Immerse  the  glass  vessel  in  the  mercury.  The  tem- 
perature of  the  water  gradually. falls  to  0°,  when  the  water  begins  to 
freeze,  and  its  temperature  becomes  constant.  The  temperature  of 
the  mercury  rises  while  the  water  is  freezing. 

234.  Solidification.  —  When  a  liquid  changes  to  a  solid, 
the  energy  that  was  employed  in  maintaining  the  charac- 
teristic freedom  of  molecular  motion  against  the  force  of 
cohesion  is  released  and  appears  as  heat.     The  amount 
of  heat  that  reappears  during  solidification  is  the  same  as 
that  which  disappears  during  liquefaction. 

235.  Laws  of  Fusion.  —  It  has  been  found  by  experi- 
ment that  the  following  statements  are  true :  — 

(1)  A  solid  begins  to  melt  at  a  certain  temperature  that 
is  invariable  for  a  given  substance  under  constant  pressure. 
This  temperature  is  called   the  melting-point  of  that  sub- 
stance.     In  cooling,  such  liquids   solidify  at  the  melting- 
point. 

(2)  TJie  temperature  of  a  melting  solid  or  of  a  solidify- 
ing liquid  remains  at  the    melting-point   until  the   change 
of  condition  is  completed. 


EFFECTS  OF  HEAT. 


289 


(3)  Substances  that  contract  on  melting  have  their  melt- 
ing-points loivered  by  pressure,  and  vice  versa. 

(a)  It  is  possible  to  reduce  the  temperature  of  a  liquid  below  the 
melting-point  without  solidification,  but  when  solidification  does 
begin,  the  temperature  quickly  rises  to  the  melting-point. 

Vaporization. 

Experiment  189.  —  Pour  a  few  drops  of  ether  upon  the  bulb  of  a 
thermometer,  or  into  the  palm  of  the  hand,  and  notice  the  rapid  fall 
of  temperature.  See  that  there  is  no  flame  near  enough  to  ignite  the 
inflammable  vapor. 

Experiment  190.  —  Wet  a  block  of  wood  and  place  a  watch-crystal 
upon  it.  A  film  of  water  may  be  seen  under  the  central  part  of  the 
glass.  Half  fill  the  crystal  with  sulphuric  ether,  and  evaporate  it 
rapidly  by  blowing  over  its  surface  a  stream  of  air  from  a  small 
bellows.  So  much  heat  disappears  that  the  watch-crystal  is  frozen  to 
the  wooden  block. 

Experiment  191.  —  In  a  vessel  of  sulphuric  ether,  place  a  test-tube 
containing  water.     Force  a  current  of  air  through  the  ether.     (Fig. 
222.)      Rapid  evaporation  is  thus  produced  and,  in  a  few  minutes, 
the    water    is    frozen.      See 
Exercise  2,  page  198. 

236.  Vaporization  is 
the  process  of  converting 
a  substance,  especially  a 
liquid,  into  a  vapor. 
This  change  of  con- 
dition may  be  effected 
by  an  addition  of  heat, 
or  by  a  diminution  of 
pressure,  or  both.  When 
it  takes  place  slowly  and 
quietly,  the  process  is 
called  evaporation.  When  it  takes  place  so  rapidly  that 
19 


FIG. 


290  SCHOOL  PHYSICS. 

the  liquid  mass  is  visibly  agitated  by  the  formation  of 
vapor  bubbles  within  it,  the  process  is  called  ebullition^ 
The  heat  that  produces  the  change  of  condition  disappears 
in  the  process. 

237.  Condensation.  —  The  liquefaction  of  gases  and  va- 
pors is  effected  by  a  withdrawal  of  heat  or  by  an  increase 
of  pressure,  or  both.     In  either  case,  the  energy  that  was 
employed  in  maintaining  the  aeriform  condition  is  released 
and  appears  as  heat.     The  amount  of  heat  that  reappears 
during  liquefaction  is  the  same  as  that  which  disappears 
during  vaporization. 

238.  Laws  of   Evaporation.  —  Experiments   show   that 
the  rapidity  of  evaporation  — 

(1)  Increases  with  a  rise  of  temperature. 

(2)  Increases  with  an  increase  of  the  free  surface  of  the 
liquid. 

(3)  Increases  as  the  atmospheric  or  other  pressure  upon 
the  liquid  decreases,  it  being  very  rapid  in  a  vacuum. 

(4)  Increases  with  the  rapidity  of  change  of  the  atmos- 
phere in  contact  with  the  liquid. 

(5)  Decreases  with  an  increase  of  the  vapor  of  the  same 
substance  in  the  atmosphere  in  contact  with  the  liquid. 

(a)  Water  may  be  frozen  by  its  own  rapid  evaporation  under  a 
low  pressure.  When  liquefied  carbon  dioxide  is  relieved  from  pres- 
sure, it  evaporates  very  rapidly ;  the  correspondingly  rapid  absorption 
of  heat  reduces  the  temperature  to  about  —90°,  and  freezes  much  of  the 
gas  to  a  snow-like  solid.  By  evaporating  liquefied  hydrogen,  a  tem- 
perature of  —243°  has  been  obtained. 

239.  Dew-Point.  —  A  space  is  said  to  be  in  a  state  of 
saturation  with  respect  to  a  vapor  when  it  contains  as 


EFFECTS   OF   HEAT.  291 

much  of  that  vapor  as  it  can  hold  at  that  temperature. 
The  vapor  then  has  the  maximum  elastic  pressure  for  that 
temperature.  The  quantity  of  vapor  required  for  satura- 
tion increases  rapidly  with  the  temperature.  When  a 
body  of  moist  air  is  cooled,  the  point  of  saturation  is 
gradually  approached;  when  it  has  been  reached,  any  fur- 
ther cooling  causes  a  condensation  of  the  vapor  to  dew, 
fog,  or  cloud,  according  to  circumstances.  The  tempera- 
ture at  ivhich  this  condensation  occurs  is  called  the  dew- 
point.  An  instrument  for  determining  the  ratio  between 
the  actual  amount  of  water  vapor  present  in  the  air,  and 
that  required  for  saturation  is  called  a  hygrometer.  The 
branch  of  physics  that  relates  to  the  determination  of  the 
humidity  of  the  atmosphere  is  called  hygrometry. 

(a)  The  ratio  between  the  amount  of  watery  vapor  present  in  the 
air  and  the  quantity  that  is  required  for  saturation  at  the  temperature 
of  observation  is  called  the  relative  humidity.  This  ratio  is  generally 
expressed  in  percentages,  as  75  per  cent,  or  0.75. 

Boiling-Point. 

Experiment  192.  —  In  a  beaker  half  full  of  water,  place  a  thermom- 
eter and  a  test-tube  half  filled  with  ether.     Heat  the  water.     When 
the  thermometer  shows  a  temperature   of  about   60°, 
the  ether  will  begin  to  boil.     The  water  will  not  boil 
until  the  temperature  rises  to  100°.     The  temperature 
will  not  rise  beyond  this  point. 

Experiment  193.  —  Place  a  thermometer  in  a  metal 
dish  half  filled  with  water,  and  place  a  lamp  beneath 
the  dish.     Be  careful  that  the  bulb  of  the  thermometer 
is  covered  with  water,  and  that  it  is  not  less   than        FIG.  223. 
4  or  5  cm.  above  the  bottom  of  the  vessel.     Notice  the 
rise  of  the  thermometer.     Soon  the  formation  and  condensation  of 
minute  steam-bubbles  in  the  liquid  will  produce  the  peculiar  sound 
known  as  singing  or  simmering,  the  well-known  herald  of  ebullition. 


292  SCHOOL  PHYSICS. 

Finally,  the  water  becomes  heated  throughout,  the  bubbles  increase 
in  number,  grow  larger  as  they  ascend,  burst  at  the  surface,  and 
disappear  in  the  atmosphere.  Notice  that  the  temperature  remains 
stationary  after  ebullition  begins. 

Experiment  194.  —  When  the  water  used  in  Experiment  193  has 
partly  cooled,  dissolve  in  it  as  much  common  salt  as  possible,  heat  it 
again,  and  notice  that  it  does  not  boil  until  the  temperature  is  notice- 
ably higher  than  before. 

240.  Laws  of  Ebullition.  —  It  has  been  found  by  experi- 
ment that  the  following  statements  are  true  :  — 

(1)  A  liquid  begins  to  boil  at  a  certain  temperature  that  is 
invariable  for  a  given  substance  under  constant  conditions. 
This  temperature  is  called  the  boiling-point  of  that  substance. 
In  cooling,  such  vapors  liquefy  at  the  boiling-point. 

(2)  The  temperature  of  the  boiling  liquid  or  of  the  lique- 
fying vapor  remains  at  the  boiling-point  until  the  change  of 
condition  is  completed. 

(3)  An  increase  of  pressure  raises  the  boiling-point,  and 
vice  versa. 

(4)  The  boiling-point  is  affected  by  the  character  of  the 
surface  of  the  vessel  containing  the  liquid,  —  an  effect  of 
cohesion. 

(5)  The  solution  of  a  salt  in  a  liquid  raises  its  boiling- 
point,  additional  energy  being  required  to  overcome  the  cohe- 
sion involved  in  the  solution. 

(a)  It  is  possible  to  heat  water  above  its  true  boiling-point  without 
ebullition,  by  confining  the  steam  and  thus  increasing  the  pressure, 
but  when  the  pressure  is  relieved,  the  superheated  vapor  immediately 
expands  and  its  temperature  is  reduced.  Hence,  in  determinations 
of  the  boiling-point,  the  thermometer  is  never  immersed  in  the  liquid 
but  in  the  vapor  just  above  it.  Strictly  speaking,  the  boiling-point  is 
the  temperature  at  which  the  elastic  force  of  the  vapor  is  equal  to  the  pres- 
sure of  the  atmosphere. 


EFFECTS   OF   HEAT. 


293 


(&)  The  temperature  of  the  water  in  a  steam-boiler  is  higher  than 
100°  whenever  the  pressure  (recorded  by  the  gauge)  is  greater  than 
one  atmosphere.  At  ten  atmospheres,  the  temperature  is  about  180°. 
Owing  to  the  effect  of  atmospheric  pressure  upon  the  boiling-point  of 
water,  the  latter  may  be  used  in  the  determination  of  altitudes  above 
the  sea-level.  A  thermometrical  barometer  for  this  purpose  consists 
of  a  portable  apparatus  for  boiling  water,  and  a  very  sensitive  ther- 
mometer, and  is  called  a  hypsometer. 

(c)  A  drop  of  water  on  a  smooth  metal  surface  at  a  high  tempera- 
ture may  rest  upon  a  cushion  of  its  own  vapor,  without  coming  into 
contact  with  the  metal.     A  liquid  in  this  spheroidal  state  is  at  a  tem- 
perature below  its  boiling-point.     When  the  metal  cools  so  that  the 
vapor  pressure  will  not  support  the   globule,  the  liquid  comes  into 
contact  with  the  metal  surface,  and  is  converted  into  steam  with  great 
rapidity.     Many  boiler  explosions  are  due  to  such  causes. 

(d)  Whenever  the  boiling-point  of  a  substance  is  lower  than  its 
melting-point,  the  substance  vaporizes  directly  without  previous  lique- 
faction.    Such  a  change  is  called  sublimation.     The  pressure  at  which 
the  melting-point  and  the  boiling-point  of  any  substance  coincide  is 
called  the  fusing-point  pressure.     If  the  fusing-point  pressure  of  a  solid 
substance  is  greater  than  the  atmospheric  pressure,  it  will  sublime 
when  heated  unless  the  pressure  upon  it  is  increased.     Carbon  dioxide 
sublimes  under  any  pressure  less  than  three  atmospheres.    Conversely, 
if  the  fusing-point  pressure  is  less  than  the  atmospheric  pressure,  sub- 
limation may  be  secured  by  reducing  the  pressure.     Iodine  sublimes 
at   pressures    less    than 

90  mm.  of  mercury,  and* 
ice  can  not  be  melted  at 
a  pressure  of  less  than 
4.6  mm.  Such  sub- 
stances evaporate  at  tem- 
peratures below  their 
melting-points. 


Distillation. 
Experiment  195.  — 
Partly  fill  with  strong 
brine  a  Florence  flask  the 
cork  of  which  carries  a 
delivery-tube  and  a  ther- 


FIG  9 


294  SCHOOL  PHYSICS. 

mometer.  Pass  the  delivery-tube  through  a  "  water  jacket/'  J,  kept 
cool  substantially  as  shown  in  Fig.  224.  Heat  the  liquid  in  the  flask 
until  it  just  boils,  and  taste  the  distilled  water  that  collects  in  R. 

Experiment  196.  —  Place  a  teaspoonful  of  alcohol  in  a  saucer  and 
apply  a  flame;  the  alcohol  burns.  Mix  50  cu.  cm.  of  alcohol  and 
50  cu.  cm.  of  water.  Test  a  teaspoonful  of  the  mixture  as  before  ;  it 
does  not  burn.  Place  the  rest  of  the  mixture  in  the  flask  of  the  appa- 
ratus described  in  Experiment  195,  and  heat  the  mixture  to  about 
90°  C.  See  if  the  liquid  that  collects  in  R  will  burn.  If  it  will  not/ 
empty  the  contents  of  R  into  F,  and  interpose  between  F  and  /  a 
bottle  that  is  partly  immersed  in  a  bath  of  boiling  water  and  repeat 
the  experiment. 

241.  Distillation  is  an  application  of  volatilization  and 
subsequent  condensation  for  various  purposes,  such  as  the 
extraction  of  the  essential  principle  of  a  substance  from 
the  liquid  in  which  it  has  been  macerated. 

(a)  The  most  common  distillation  process  consists  in  placing  the 
distillable  liquid  in  a  metal  retort,  generally  made  of  copper.     When 
heat  is  applied,  vapors  rise  into  the  movable  head  of  the  retort,  the 
neck  of  which  is  connected  with  a  spiral  tube  called  the  "worm." 
The  worm  being  kept  cool  by  flowing  water,  the  vapors  of  the  more 
easily  volatile  constituents  of  the  liquid  pass  into  it,  are  condensed, 
and  make  their  exit  as  a  liquid,  while  the  solid  and  non-volatile  liquid 
constituents  remain  behind  in  the  retort.     The  whole  apparatus  is 
called  a  "  still." 

(b)  Fractional  distillation  is  the  process  of  separating  liquids  that 
have  different  boiling-points.     The  mixture  is  heated  in  a  retort  that 
allows  constant  observation  of  the  temperature,  and  the  distillates 
obtained  between  certain  temperatures  are  collected  separately.     The 
most  volatile  constituent  of  the  mixture  will  be  found  chiefly  in  the 
"  fractions  "  first  collected.     By  redistillation  of  the  first  fraction,  this 
more  volatile   liquid  may  be  obtained  in  comparative  or  absolute 
purity. 


EFFECTS   OF   HEAT.  295 


CLASSROOM  EXERCISES. 

1.  At  high  elevations,  water  boils  at  temperatures  too  low  for  ordi- 
nary culinary  purposes.     How  may  persons  living  there  heat  water 
sufficiently  for  boiling  meats  and  vegetables  ? 

2.  For  the  extraction  of  gelatine  from  bones  by  the  action  of  hot 
water,  a  higher  temperature  than  100°  is  required.     How  may  the 
water  be  heated  sufficiently  for  such  purposes  ? 

3.  In  sugar  refining,  it  is  desirable  to  evaporate  the  saccharine 
liquid  at  a  temperature  considerably  lower  than  100°.     Indicate  a 
way  in  which  this  may  be  done. 

4.  Under  ordinary  pressure  can  ice  be  made  warmer  than  0°  ? 

5.  Solid  type-metal  floats   on   melted  type-metal.     Does   melted 
type-metal  expand  or  contract  on  solidifying?     What  effect  has  this 
quality  upon  the  use  of  the  metal  in  making  type  ? 

6.  At  the  summit  of  Mount  Washington,  water  boils  at  a  tempera- 
ture of  about  94° ;  at  the  summit  of  Mont  Blanc,  at  86° ;  at  the  level 
of  the  Dead  Sea,  at  101°.     Explain  these  differences  in  the  boiling- 
points  of  water. 

7.  If  the  smooth,  dry  surfaces  of  two  pieces  of  ice  are  pressed 
together  for  a  few  seconds,  the  pieces  will  be  frozen  together  when  the 
pressure  is  removed.     Explain  this  result,  which  is  called  regelation. 

8.  When  the  air  of  a  room  is  artificially  heated,  the  temperature 
may  become  considerably  higher  than  the  dew-point  of  the  air  in  the 
room.     Under  such  circumstances,  the  rapid  evaporation  of  moisture 
from  the  person  causes  a  disagreeable  sensation  in  the  lips,  tongue, 
skin,  etc.     How  may  sucfi  results  be  avoided  ? 

9.  Sulphur  begins  to  melt  at  115°.      At  what  temperature  does 
melted  sulphur  begin  to  solidify  ? 

10.  How  may  sea-water  be  made  fit  for  drinking? 

11.  A  drop  of  water  may  be  placed  on  a  very  hot  platinum  plate, 
and  the  plate  so  held  that  a  candle-flame  may  be  seen  between  the 
water  and  the  plate.     Explain. 

12.  How  may  a  thermometer,  a  fire,  and  a  dish  of  water,  be  used  to 
determine  the  elevation  of  a  place  above  the  sea-level  ? 

13.  Water  standing  in  a  slightly  porous  vessel  acquires  a  tempera- 
ture lower  than  that  of  the  surrounding  atmosphere.     Explain. 

14.  The  temperature  of  islands  and  of  the  borders  of  the  ocean 
and  great  lakes  is  more  equable  than  that  of  inland  regions  of  the 
same  latitude.     Point  out  the  dependence  of  this  fact  upon  the  physi- 
cal properties  of  water. 


296  SCHOOL   PHYSICS. 

15.  The  inner  surface  of  the  upper  part  of  a  bottle  that  contains 
iodine  or  gum-camphor  is  generally  covered  with  minute  crystals. 
What  conclusion  concerning  the  physical  properties  of  iodine  and 
camphor  do  you  draw  from  this  fact  ? 

16.  What  effect  has  the  humidity  of  the  atmosphere  upon  the 
dew-point  ? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Two  air  thermometers;  kerosene;  hy- 
drometer jar  with  perforations  and  jacket;  candle;  expansion  appa- 
ratus as  described  below ;  one  of  the  thin,  nickel-plated,  brass  vessels, 
larger  at  the  top  than  at  the  bottom,  such  as  are  sold  at  hardware 
stores  as  lemonade  "  shakers." 

1.  Connect  a  small  glass  funnel  by  rubber  tubing  to  the  stem  of  an 
air  thermometer.     (Fig.  224.)     The  diameter  of  the  bulb  should  be 
4  or  5  cm.  and  the  bore  of  the  stem,  3  or  4  mm.     Pour  water  into  the 
funnel  and  work  it  down  with  a  wire  until  the  bulb  is  full  and  the 
liquid  stands  at  the  height  of  about  2  cm.  in  the  stem.     Similarly,  fill 
a  like  bulb  with  kerosene.     Immerse  both  bulbs  in  water  almost  boil- 
ing-hot.    Notice  the  liquid  levels  in  the  stems  at  the  instant  of  im- 
mersion and  a  few  minutes  later.     Record  all  of  your  conclusions  from 
the  observed  phenomena,  not  omitting  to  state  what  was  measured  by 
the  rise  of  the  liquids  in  the  stems. 

2.  Drill  a  hole  through  the  wall  of  a  tall  hydrometer  jar  near  its 
top   and  another  near  the  bottom.     Close  the  holes  with  perforated 
corks  carrying  thermometers,  so  that  the  bulbs  of  the  thermometers 
shall  be  inside  the  jar.     Fill  the  jar  with  ice-cold  water  and  notice 
that  the  thermometers  give  like  readings.     As  the  water  is  warmed 
to  the  temperature  of  the  room,  observe  the  thermometers,  record  your 
observations,  and  explain  any  change  in  the  thermometric  readings, 
and  any  difference  between  the  readings  of  the  two  thermometers. 

3.  Around  the  middle  of  the  hydrometer  jar  mentioned  in  Exer- 
cise  2,  place   a  jacket  and  fill  the  jacket  with  a  mixture  of  finely 
broken  ice  and  salt.     Record  and  explain  changes  in  thermometric 
.readings  as  before. 

4.  On  a  day  when  the  doors  and  windows  are  closed,  ascertain  the 
temperature   of  the  laboratory  near  the  ceiling  and  near  the  floor. 
Record  your  observations  and  explain  any  difference  that  you  find. 

5.  On  a  day  when  the  air  in  the  laboratory  is  warmer  than  that 
outside,  stand  an  outer  door  slightly  ajar,  and  with  a  candle  flame, 


EFFECTS  OF   HEAT. 


297 


seek  for  inward  and  outward  air-currents.  If  you  find  them,  explain 
their  production  and  show  that  they  have  an  important  relation  to 
artificial  ventilation. 

6.  Half  fill  a  Florence  flask  with  water.     Boil  the  water  until  the 
steam  drives  the  air  from  the  upper  part  of  the  flask.     Cork  the  flask  so 
that  no  air  can  enter,  and  quickly  remove  the  lamp.      Support  the 
inverted  flask  upon  the  ring  of  a  retort  stand  and  place  a  pan  below 
it.     By  this  time,  the  water  will  have  stopped  boiling.     Pour  cold 
water  upon  the  flask.     Record   and   explain   the   consequent  phe- 
nomena.    Without  again   heating  the  water,  repeat  the  drenching 
several  times  and  finally  immerse  the  flask  in  cool  water. 

7.  Get  a  cylindrical  tube,  cd  (Fig.  225),  made  of  "  galvanized  "  iron 
or  other  sheet  metal.    It  should  be  about  2.5  cm.  in  diameter  and  about 
60  cm.  long.     Near  each  end  of  the  tube,  insert  a  tube  about  6  mm.  in 
diameter  and  about  3  cm.  long,  as  shown  at  a  and  i.     At  the  middle  of 
the  main  tube,  insert  a  tube  about  1.5  cm.  in  diameter  and  about  1  cm. 
long,  as  shown  at  e.     Get  a  brass  tube  about  6  mm.  in  diameter  and 
about  6  mm.  longer  than  the  tube,  cd.     Solder  a  fine  steel  wire  in  a 


FIG.  225. 


diametral  position  across  one  end  of  the  brass  tube.  Accurately 
measure  the  length  of  the  brass  tube  and  place  that  tube  inside  the 
larger  tube  so  that  it  shall  be  supported  by  short  perforated  corks 
that  close  the  ends  of  the  latter.  The  end  that  carries  the  steel  wire 
should  be  at  the  end  of  the  jacket  marked  c.  Upon  a  baseboard 
about  1  m.  long  and  15  cm.  wide,  erect  five  posts,  s,  x,  m,  n  and  w.  As 
m  and  n  are  to  carry  the  brass  tube  and  its  jacket,  they  have  V-shaped 
notches  at  their  upper  ends ;  m  is  made  a  few  millimeters  longer  than 
n,  so  that  the  water  of  condensation  will  run  out  at  i.  A  common  flat- 
headed  screw  is  set  in  the  vertical  face  of  w  so  that,  when  the  jacket  is 
in  position,  the  end  of  the  brass  tube  will  rest  against  the  head  of 
the  screw.  The  distance  between  w  and  x  is  such  that  the  latter  may 
carry  a  right-angled  lever,  I,  with  its  short  arm  resting  in  a  vertical 


298  SCHOOL  PHYSICS. 

position  against  the  wire  soldered  to  the  end  of  the  brass  tube.     This 
lever  may  be  made  of  a  tapering  piece  of  wood  about  1.5  cm.  square 

near  the  fulcrum  end.  A  "  machine  " 
screw  set  into  the  face  of  x  makes  a 
good  fulcrum.  The  short  arm  of 
the  lever  should  be  faced  with  a 
metal  strip,  the  free  surface  of  which 
lies  in  a  vertical  line  through  the 
center  of  the  fulcrum  when  the  long 
arm  is  horizontal.  A  metal  casting 
of  the  shape  indicated  by  Fig.  226, 

Fi     226      t~" J  *S  Desirable  f°r  carrying  the  index- 

arm  of  the  lever.  The  lever  should 
turn  upon  the  fulcrum  screw  by  its  own  weight  but  without  looseness. 
The  post,  s,  carries  a  millimeter  scale  over  which  the  long  arm  of  the 
lever  moves.  The  large  tube  may  be  kept  from  turning  upon  its  axis 
by  a  peg  inserted  in  x,  to  which  the  tube  at  a  may  be  tied. 

Place  the  large  tube  in  position.  Adjust  the  brass  tube  so  that  it 
projects  about  3  mm.  at  each  end  and  so  that  the  steel  wire  is  hori- 
zontal. When  the  short  arm  of  the  bent  lever  rests  against  the  steel 
wire,  adjust  the  screw  in  w  until  the  long  arm  of  the  lever  is  hori- 
zontal. Pass  the  bulb  of  a  thermometer  through  a  perforated  cork 
that  closes  the  short  tube  at  e;  do  not  let  it  touch  the  brass  tube. 
Place  a  tumbler  below  the  exit  tube  at  i.  Connect  the  inlet  tube 
at  a,  by  a  piece  of  rubber  tubing  75  or  80  cm.  long,  to  the  boiler 
described  in  Exercise  3,  page  275,  and  shield  the  adjusted  apparatus 
from  the  heat  of  the  lamp  and  boiler.  Then  measure  the  horizontal 
distance  from  the  center  of  the  fulcrum  screw  to  the  edge  of  the 
millimeter  scale  from  which  readings  are  to  be  taken,  and  the  verti- 
cal distance  from  the  center  of  the  same  screw  to  the  steel  wire  at 
the  end  of  the  brass  tube,  and  find  the  ratio  between  the  two  dis- 
tances. This  ratio  should  be  not  less  than  20.  Note  the  reading  of 
the  scale  and  the  temperature  inside  the  jacket.  Generate  steam  in  the 
boiler  and  let  it  flow  through  the  jacket  for  a  few  minutes  after  the 
mercury  has  ceased  to  rise  in  the  thermometer.  When  the  movement 
of  the  long  arm  of  the  lever  ceases,  take  the  readings  of  the  millimeter 
scale,  the  thermometer,  and  the  barometer.  Test  the  accuracy  of  the 
thermometric  reading  by  the  temperature  as  computed  from  the  boil- 
ing-point of  water  at  the  observed  atmospheric  pressure.  Detach  the 
rubber  tube  at  a  and  allow  the  apparatus  to  cool.  Press  the  brass 


THE   MEASUREMENT  OF   HEAT.  299 

tube  against  the  head  of  the  screw  in  w  and  see  if  the  index  returns 
to  its  original  position,  as  it  should.  From  the  data  obtained,  calcu- 
late the  coefficients  of  linear  and  cubical  expansion  for  brass. 

Represent  the  actual  elongation  of  the  bar  by  e ;  the  temperature 
observed  at  the  beginning  of  the  experiment  by  t ;  the  highest  tem- 
perature by  t' ;  the  length  of  the  brass  tube  before  heating  by  I; 
and  the  coefficient  of  linear  expansion  by  k.  Then  we  have,  by 
definition :  — 

*  =  (t'-t)i'  whence  e  =  k  (i'~  °  lm 

This  last  algebraic  expression  shows  why  k  is  called  a  coefficient. 

8.  Determine  the  boiling-point  of  a  saturated  solution  of  saltpeter. 

9.  Put  a  little  water  at  the  temperature  of  the  laboratory  into  a 
nickel-plated  cup,  the  outer  surface   of  which  should  be   brightly 
polished.     Breathe  upon  the  polished  surface,  and  notice  that  the 
moisture-film  is  evanescent.      Place  the  bulb  of  a  thermometer  in 
the  water  and  add  ice.      Stir  the  mixture  continually.      Note  the 
temperature  of  the  cooling  water  at  the  moment  when  the  moisture- 
film  clearly  appears  on  the  outer  surface  of  the  cup  at  a  point  that 
cannot  be  affected  by  your  breath.     K  the  ice  is  not  all  melted, 
remove  the  residue  from  the  cup.     As  the  water  slowly  warms,  note 
the   temperature   at  which  the   moisture-film   begins   to  disappear. 
Take  the  mean  of  the  two  observed  temperatures  and  call  it  the 
"dew-point."     To  your  other  records,  add  your  observation  of  the 
weather  and  the  out-door  temperature. 


IV,    THE  MEASUREMENT  OF  HEAT. 

242.  Calorimetry   is    the    process    of    measuring    the 
amount   of   heat   that   a   body  absorbs  or   gives    out   in 
passing  through  a  change  of  temperature  or  of  physical 
condition. 

243.  A   Thermal  Unit,   or  a  heat-unit,  is   the   quantity 
of  heat  required  to  raise  the  temperature  of  unit  mass  of 
water  one  degree.     The  unit  most  commonly  used  is  the 


300  SCHOOL  PHYSICS. 

quantity  of  heat  required  to  raise  the  temperature  of  one 
gram  of  water  from  0°  to  1°.  This  water-gram-degree  unit 
is  called  a  therm,  or  a  small  calory. 

(a)  A  large  calory  is  the  quantity  of  heat  required  to  raise  the 
temperature  of  a  kilogram  of  water  from  0°  to  1°.  Unless  otherwise 
specified,  the  calory  mentioned  in  this  book  is  the  small  calory. 

244.  Latent  Heat.  —  In  considering  changes  of  condition 
of  matter,  we  have  spoken  of  the  disappearance  and  re- 
appearance of  heat.     When  heat  thus  disappears,  molec- 
ular kinetic  energy  is  transformed  into  the  potential  form ; 
when  it  reappears,  the  reverse  transformation  takes  place. 
Because  this  molecular  kinetic  energy  affects  temperature, 
it  is  called  sensible  heat.     Because  this  molecular  potential 
energy  does  not  affect  temperature,  it  is  called  latent  heat. 

(a)  So  much  of  the  added  heat  as  is  used  to  increase  the  rapidity 
of  molecular  motions  is  kinetic  and  appears  as  sensible  heat.  So 
much  of  it  as  is  used  to  oppose  cohesion  (disgregation)  and  to 
overcome  pressure  becomes  potential,  and  disappears  as  latent  heat. 
When  ether  evaporates,  the  potential  energy  needed  to  establish  the 
aeriform  condition  is  obtained  by  the  transformation  of  kinetic  energy 
and  at  the  expense  thereof;  hence,  the  disappearance  of  sensible  heat, 
or  the  fall  of  temperature.  When  steam  is  condensed,  the  potential 
energy  that  is  no  longer  required  to  maintain  the  aeriform  condition 
is  transformed  into  kinetic  energy;  hence,  the  increase  of  sensible 
heat.  These  terms,  "  sensible  "  and  "  latent,"  are  reminiscences  of  the 
old  theory  that  heat  is  a  kind  of  matter. 

Experiment  197.  —  Add  a  kilogram  of  finely  broken  ice  (0°)  to  a 
kilogram  of  water  at  80°.  The  ice  will  melt,  and  the  temperature  of 
the  two  kilograms  of  water  will  be  about  0°.  The  80,000  calories 
given  out  by  the  hot  water  were  used  in  simply  melting  the  ice. 

245.  The  Latent  Heat  of  Fusion  of  a  substance  is  the 
quantity  of  heat  that  is  required  to  melt  one  gram  of  the 
substance  without  raising  its  temperature  ;  i.e.,  the  quantity 


THE   MEASUREMENT  OF  HEAT.  301 

of  heat  that  is  expended  in  the  molecular  work  involved 
in  the  change  from  the   solid   to   the   liquid  condition. 
The  latent  heat  of  fusion  of  ice  is  about  eighty  calories. 
Ice  at  0°  +  latent  heat  of  fusion  =  water  at  0°. 

(a)  From  the  above  statement  it  necessarily  follows  that  the  heat 
required  to  melt  any  weight  of  ice  would  warm  80  times  that  weight 
of  water  one  degree,  or  the  same  weight  of  water  80  degrees,  provided 
there  was  no  change  of  physical  condition. 

Experiment  198.  —  To  the  end  of  the  delivery- tube  of  a  Florence 
flask  containing  water,  attach  a  "  trap  "  like  that  shown  in  Fig.  227, 
so  that  the  water  that  condenses  in  the  delivery-tube  may  be  retained 
in  the  trap.  (Instead  of  using  the  trap,  th'e  delivery-tube  may  be  kept 
hot  by  a  steam-jacket,  for  which  purpose  the  apparatus  shown  in  Fig. 
224  or  Fig.  225  may  be  easily  adapted.)  Boil  the  water,  and  when 
steam  passes  rapidly  from  a,  the  lower  tube  of  the  trap,  dip  a  into  a 
beaker  of  known  weight  and  containing  water  of  known 
weight  and  temperature.  The  temperature  of  the  water  in 
the  beaker  should  be  considerably  lower  than  that  of  the  room, 
and  the  end  of  the  tube  that  leads  steam  from  the  trap  to  the 
beaker  should  not  dip  into  the  wrater  so  much  that  the  con- 
densation of  the  steam  may  not  be  plainly  heard.  The  beaker 
should  be  covered  with  a  piece  of  cardboard,  perforated  for 
the  admission  of  the  tube,  a,  and  of  the  thermometer,  and 
should  be  shielded  from  the  heat  of  the  lamp  and  flask. 
After  the  flow  of  steam  has  been  continued  for  some  time, 
remove  the  beaker,  stir  its  contents  with  the  thermometer  FIG. 

227 

thoroughly,  and  take  the  temperature  quickly  but  carefully. 
Ascertain  the  exact  increase  in  the  weight  of  the  water  in  the 
beaker,  and  compute  the  amount  of  heat  derived  from  the  conden- 
sation of  each  gram  of  steam.  Suppose  that  at  the  beginning  of  the 
experiment  the  water  in  the  beaker  weighed  400  g.,  and  had  a  tem- 
perature of  0°,  and  that  at  the  end  of  the  experiment  the  weight 
,was  420  g.,  and  the  temperature  30°.  The  400  g.  of  water  received 
12,000  calories  that  came  from  the  20  g.  of  steam.  In  cooling  from 
100°  to  30°,  the  condensed  steam  parted  with  1,400  calories.  The 
remaining  10,600  calories  came  from  the  latent  heat  of  the  steam ; 
i.e.,  each  gram  of  steam  at  100°  gave  out  530  calories  in  condensing 
to  water  at  the  same  temperature.  This  result  is  subject  to  correc- 
tion for  radiation,  absorption,  etc. 


302  SCHOOL   PHYSICS. 

246.  The  Latent  Heat  of  Vaporization  of  a  substance  is 
the  quantity  of  heat  that  is  required  to  vaporize  one  gram 
of  that   substance    without   raising   its   temperature.     The 
latent  heat   of   the  vaporization  of   water   is   about  537 
calories. 

Water  at  100°  -f  latent  heat  of  vaporization  =  steam  at 
100°. 

(a)  From  the  above  statement  it  necessarily  follows  that  the  heat 
required  to  vaporize  any  weight  of  water  would  warm  537  times  that 

weight  of  water  one  degree,  or  n  times  that  weight  of  water  - 
degrees,  provided  there  was  no  change  of  physical  condition. 

Experiment  199.  —  Cut  a  piece  of  sheet  lead  about  5  x  30  cm.,  wind 
it  into  a  loose  roll,  and  suspend  it  by  a  thread  in  a  vessel  of  boiling 
water.  In  a  few  minutes  the  lead  will  have  the  temperature  of  100°. 
Transfer  the  lead  to  a  thin  metal  vessel,  containing  a  weighed  quantity 
of  water  sufficient  to  cover  the  lead,  and  of  known  temperature.  Stir 
the  water  with  a  thermometer,  and  note  the  temperature  of  the  water 
when  it  reaches  its  maximum.  Multiply  the  weight  of  the  warmed 
water  by  its  increase  of  temperature,  to  ascertain  the  number  of 
calories  transferred  by  the  lead.  Divide  the  number  of  calories  by 
the  fall  of  the  temperature  of  the  lead,  to  find  the  heat  capacity  of  the 
lead  roll.  Divide  this  capacity  by  the  weight  of  the  lead,  to  find 
the  specific  heat  of  lead.  Remember  that,  for  work  of  precision,  such 
results  would  have  to  be  corrected  for  radiation,  absorption  by  the 
vessel,  etc. 

247.  The  Specific  Heat  of  a  substance  is  the  ratio  between 
the  amount  of  heat  required  to  raise  the  temperature  of  any 
weight  of  that  substance  one  degree,  and  the  amount  of  heat 
required  to  raise  the  temperature  of  the  same  weight  of  water 
one  degree.     It  indicates  the  number  of  calories  absorbed 
or  emitted  by  one  gram  of  that  substance  while  under- 
going a  change  of  one  degree  of  temperature. 


THE   MEASUREMENT  OF   HEAT.  303 

(a)  The  force  of  cohesion  differs  considerably  for  different  sub- 
stances.    Consequently,  when  heat  is  added,  the  part  thereof  that  is 
employed  against  cohesion  in  giving  new  positions  to  the  molecules, 
and  that  is  thus  transformed  from  kinetic  to  potential  energy  (i.e., 
from  sensible  to  latent  heat),  is  different  for  different  substances. 
The  quantities  of  sensible  heat  remaining  after  such  transformations 
being  thus  different,  the  several  substances  have  different  specific 
heats. 

(b)  The  specific  heat  of  hydrogen  is  3.409  ;  of  ice,  0.505;  of  steam, 
0.48;  of  oxygen,  0.2175;  of  iron,  0.1138;  of  lead,  0.0314.     Water  in 
its  liquid  form  has  a  higher  specific  heat  than  any  other  substance 
except  hydrogen. 

Experiment  200.  —  Pour  400  cu.  cm.  of  water  at  the  temperature 
of  20°  into  400  cu.  cm.  of  water  at  the  temperature  of  60°,  and  con- 
tained in  a  thin  liter  flask.  The  temperature  of  the  mixture  will  not 
vary  much  from  40°.  Remember  that  allowance  must  be  made  for 
loss  of  heat  by  radiation  and  for  absorption  of  heat  by  the  vessel. 
The  cool  water  gains  and  the  warm  water  loses  equal  amounts  of 
heat;  i.e.,  8,000  calories;  the  thermal  capacity  of  water  is  practically 
the  same  at  different  temperatures. 

248.  The  Thermal  Capacity  of  a  body  is  the  number  of 
calories  required  to  raise  its  temperature  one  degree.  It  is 
the  product  of  the  mass  into  the  specific  heat,  and  has 
direct  reference  to  the  amount  of  heat  the  body  absorbs 
or  gives  out  in  passing  through  a  given  range  of  tempera- 
ture. 

CLASSROOM  EXERCISES. 

1.  One  kilogram  of  water  at  40°,  2  Kg.  at  30°,  3  Kg.  at  20°,  and 
4  Kg.  at  10°,  are  thoroughly  mixed.     Find  the  temperature  of  the 
mixture.  Ans.  20°. 

2.  One  pound  of  mercury  at  20°  was  mixed  with  one  pound  of 
water  at  0°,  and  the  temperature  of  the  mixture  was  0.634°.     Calcu- 
late the  specific  heat  of  mercury. 

3.  What  weight  of  water  at  85°  will  just  melt  15  pounds  of  ice 
at  0°?  Ans.  14.117  pounds. 


SCHOOL  PHYSICS. 

4.  What  weight  of  water  at  95°  will  just  melt  10  pounds  of  ice 
at  -  10°?  Am.  8.947  pounds. 

5.  What  weight  of  steam  at  125°  will  melt  5  pounds  of  ice  at  -  8°, 
arid  warm  the  water  to  25°  V 

6.  How  many  grams  of  ice  at  0°  can  be  melted  by  1  g.  of  steam  at 
100°? 

7.  Equal  masses  of  ice  at  0°  and  hot  water  are  mixed.     The  ice  is 
melted,  and  the  temperature  of  the  mixture  is  0°.     What  was  the 
temperature  of  the  water  ? 

8.  Ice  at  0°  is  mixed  with  ten  times  its  weight  of  water  at  20°. 
Find  the  .temperature  of  the  mixture.  Ans.  11°  nearly. 

9.  One  pound  of  ice  at  0°  is  placed  in  5  pounds  of  water  at  12°. 
What  is  the  result? 

10.  What  temperature  will  be  obtained  by  condensing  10  g.  of 
steam  at  100°  in  1  Kg.  of  water  at  0°? 

11.  A  gram  of  steam  at  100°  is  condensed  in  10  grams  of  water  at 
0°.     Find  the  resulting  temperature.  A  ns.  58°  nearly. 

12.  If  200  g.  of  iron  at  300°  is  plunged  into  1  Kg.  of  water  at  0°, 
what  will  be  the  resulting  temperature?  Ans.  C.67°. 

13.  A  body  with  a  weight  of  80  g.,  and  a  temperature  of  100°,  is 
immersed  in  200  g.  of  water  at  10°,  and  raises  the  temperature  of  the 
water  to  20°.     What  is  the  specific  heat  of  the  body  ? 

14.  How  many  pounds  of  steam  at  100°  will  just  melt  100  pounds 
of  ice  at  0°?  Ans.  12.55  +  pounds. 

15.  What  will  be  the  result  of  mixing  5  ounces  of  snow  at  0°  with 
23  ounces  of  water  at  20°? 

16.  What  weight  of  steam  at  100°  would  be  required  to  raise  the 
temperature  of  500  pounds  of  water  from  0°  to  10°  ?    A  ns.  7.97  pounds. 

17.  What  weight  of  mercury  at  0°  will  be  warmed  one  degree  by 
placing  in  it  150  g.  of  lead  at  300°? 

18.  If  4  pounds  of  steam  at  100°  is  mixed  with  200  pounds  of  water 
at  10°,  what  will  be  the  resultant  temperature  ? 

19.  A  pound  of  sulphur  can  melt  only  one-fifth  as  much  ice  as  a 
pound  of  water  at  the  same  temperature.     What  does  this  show  con- 
cerning the  specific  heats  of  water  and  sulphur  ? 

20.  Explain  the  difference  between  thermal  capacity  and  specific 
heat. 

21.  If  there  was  no  water  on  the  earth,  would  the  differences  in 
temperature  between  day  arid  night,  and  between  summer  and  winter, 
be  greater  or  less  than  they  now  are  ?     Why  ? 


THE   MEASUREMENT   OF   HEAT.  305 

22.  From  a  good  dictionary  or  any  other  available  source  of  infor- 
mation, get   an   idea  of  the   operation   of  an  ice-machine  or  of  a 
refrigerating  machine,  and  then  show  that  when  work  is  done  upon 
a  gas  there  is  an  increase  of  sensible  heat,  and  that  when  work  is 
done  by  a  gas  there  is  a  decrease  of  sensible  heat. 

23.  Tubs  of  water  are  sometimes  placed  in  cellars  to  "keep  the 
frost  away "  from  vegetables,  the  f reezing-point  of  which  is  a  little 
below  0°.     Explain  the  effect  of  the  water  in  this  respect. 

24.  The  cylinder  of  a  pump  that  forces  air  into  the  pneumatic  tire 
of  a  bicycle  is  heated  in  the  process.     Explain. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  — 1.5  Kg.  of  mercury;  5  balls  of  dif- 
ferent metals,  each  about  an  inch  in  diameter ;  a  cake  of  beeswax ;  a 
copper  dipper  as  described  below;  1£  pounds  of  Xo.  13  shot;  ice 
or  snow. 

1.  Pour  quickly,  and  through  the  shortest  possible  air  space,  1.5 
Kg.  of  mercury  at  100°,  into  500  g.  of  water  at  0°.     Stir  the  liquids 
thoroughly  together  with  a  thermometer,  and,  from  the  resultant 
temperature,  determine  the  specific  heat  of  mercury. 

2.  Place  small  and  similar  balls  made  severally  of  iron,  copper,  tin, 
lead,  and  bismuth,  in  a  bath  of  linseed  oil,  and  heat  them  to  a  tem- 
perature of  180°,  or  200°.     When  they  have  all  had  time  to  acquire 
the  temperature  of  the   bath,  wipe  them  dry,  place  them  upon  a 
cake  of  beeswax  about  half  an  inch  thick,  and,  from  what  you  see, 
arrange  the  five  metals  in.  the  order  of  their  several  specific  heats. 

3.  Provide  a  sheet-copper  dipper,  4  cm.  in  diameter,  and  10  cm. 
deep,  and  encircled  about  2  cm.  from  the  top  by  a  flat  flange  of  the 
same   material,  and   about  4  cm.   wide.      A   handle 

should  be  fastened  to  this  flange.  Accurately  deter- 
mine the  weight  of  the  "  shaker  "  used  in  Exercise  9, 
page  299,  which  we  shall  hereafter  call  a  calorimeter. 

H*T         OOft 

Into  the  dipper,  put  about  500  g.  of  very  fine  shot 
that  has  been  accurately  weighed.  Fill  the  cylindrical  part  of 
the  boiler  described  in  Exercise  3,  page  275,  to  the  depth  of  about 
6  cm.  with  water,  and  cork  the  side  tube,  a.  Place  the  dipper  in  the 
boiler,  the  flange  of  the  dipper  resting  upon  the  top  of  the  boiler. 
Cover  the  dipper  with  a  piece  of  cardboard  that  has  a  hole,  through 
which  push  the  bulb  of  a  thermometer  down  into  the  shot.  Boil  the 
20 


306  SCHOOL  PHYSICS. 

water,  stir  the  shot  frequently  and  thoroughly  with  any  convenient 
instrument,  and  observe  the  rise  of  temperature  of  the  shot. 

Put  about  100  cu.  cm.  of  water  into  the  calorimeter.  Cool  the 
water  with  ice  or  snow  until  its  temperature  is  7  or  8  degrees  below 
that  of  the  laboratory.  When  the  mercury  column  of  the  thermome- 
ter becomes  stationary,  note  the  temperature  of  the  shot.  Remove 
the  thermometer,  and  allow  it  to  cool  in  air  to  about  40°,  and  then 
ascertain  the  temperature  of  the  water  in  the  calorimeter,  stirring  the 
water  with  a  thermometer  until  the  thermometer  and  all  parts  of  the 
water  have  a  uniform  temperature.  In  the  meantime,  stir  the  shot  at 
frequent  intervals.  Bring  the  mouth  of  the  dipper  to  the  mouth  of 
the  calorimeter,  and  quickly  pour  the  shot  into  the  water,  being  care- 
ful not  to  spill  the  shot  or  to  splash  the  water.  Stir  the'  shot  and 
water  quickly  and  thoroughly,  and  take  the  temperature  of  the  con- 
tents of  the  calorimeter.  Weigh  the  calorimeter  and  its  contents, 
and,  deducting  the  weights  of  the  vessel  and  the  shot,  ascertain  the 
weight  of  the  water  heated  by  the  shot.  From  the  data  now  secured, 
calculate  the  specific  heat  of  lead.  Remember  that  for  work  of  pre- 
cision, corrections  would  have  to  be  made  for  the  loss  of  heat  by 
radiation,  and  by  absorption  by  the  calorimeter,  etc. 

4.  Repeat  Exercise  3,  using  brass-filings  instead  of  shot. 


V.    THE  RELATION   BETWEEN  HEAT  AND  WORK. 

249.    Correlation   of   Heat   and    Mechanical   Energy.  - 

When  heat  is  produced,  some  other  kind  of  energy 
disappears,  and  vice  versa.  The  most  important  of  these 
transformations  are  those  between  heat  and  mechanical 
energy.  We  are  able  to  effect  a  total  conversion  of 
mechanical  energy  into  heat,  but  we  are  not  able  to 
bring  about  a  total  conversion  of  heat  into  mechanical 
energy. 

Experiment  201.  —  Pass  a  bent  glass  tube  through  the  air-tight 
cork  of  a  flask  half  full  of  water,  and  let  it  dip  beneath  the  surface  of 


THE  RELATION  BETWEEN  HEAT  AND  WORK.   307 


the  water.     Heat  the  flask.     The  heat  will  raise  some  of  the  water  to 
the  end  of  the  tube,  where  it  may  be 
caught  as  shown  in  Fig.  229. 

Experiment  202.  —  To  the  spindle 
of  a  whirling-table,  attach  a  brass  tube 
about  10  cm.  long  and  closed  at  the 
lower  end.  Partly  fill  the  tube  with 
alcohol  and  cork  the  open  end.  Press 
the  tube  between  two  pieces  of  board 
hinged  together  as  shown  in  Fig.  230. 
The  grooves  on  the  inner  faces  of  the 
boards  should  be  faced  with  leather. 
Rotate  the  apparatus,  pressing  with 
the  clamp  upon  the  tube.  Friction 
transforms  the  mechanical  energy 
into  heat,  and  the  vapor  from  the 
alcohol  thus  boiled  may  drive  out  the  cork  with  explosive  violence. 


FIG.  229. 


FIG.  230. 

250.  Joule's  Principle.  —  The  disappearance  of  a  definite 
amount  of  mechanical  energy  is  accompanied  by  the  produc- 
tion of  an  equivalent  amount  of  heat. 

251.  —  The  Mechanical  Equivalent  of  Heat  signifies  the 
numerical  relation  beticeen  work-units  and  equivalent  heat- 


308 


SCHOOL  PHYSICS. 


units.  The  quantity  of  heat  that  will  raise  the  tempera- 
ture of  one  pound  of  water  one  Fahrenheit  degree  is 
equivalent  to  about  778  foot-pounds.  For  centigrade 
degrees  the  equivalent  is  1.8  times  as  great,  or  about  1,400 
foot-pounds.  The  mechanical  equivalent  of  a  calory  is 
about  427  gram-meters,  or  4.2  x  107  ergs. 

252.    The    Heat   Equivalent  of  Chemical   Union  has   a 

determinative  relation  to  the  comparative  fuel-values 
of  substances. 

(a)  The  numerical  values  given  below  indicate  that  the  combustion 
of  a  given  weight  of  the  substance  in  oxygen  yields  heat  enough  to 
warm  so  many  times  its  own  weight  of  water  one  centigrade  degree, 
or  1.8  times  that  many  Fahrenheit  degrees.  For  example,  the  com- 
bustion of  a  gram  of  pure  carbon  develops  8,080  calories :  — 


Hydrogen  . 
Petroleum 


34,462 
12,300 


Carbon 8,080 

Alcohol 6,850 


253.    The  Steam  Engine  is  a  powerful  device  for  utiliz- 
ing the  energy  involved  in  the  elasticity  and  expansive 

force  of  steam  as  a  mo- 
tive power.  It  is  a  real 
heat-engine,  transform- 
ing heat  into  mechanical 
energy.  In  its  modern 
forms,  it  has  many  com- 
plicated accessories  for 
increasing  its  efficiency 
and  adapting  it  to  the 
special  uses  to  which  it 
is  put,  but  the  funda- 
mentally important  parts 
are  the  cylinder,  piston,  and  slide-valve,  diagrammatically 


FIG.  231. 


THE   RELATION  BETWEEN   HEAT  AND   WORK.       309 


represented  in  Figs.  231  and  232,  in  which  the  steam- 
chest  is  represented  as  being  at  a  distance  from  the 
cylinder,  simply  for  the  purpose  of  making  clear  the  com- 
municating steam  passages.  The  piston,  P,  is  moved  to 
and  fro  in  the  cylinder  by  the  pressure  of  the  steam 
which  is  applied  to  its  two  faces  alternately.  This  alter- 
nate application  of  the  steam  pressure  is  effected  by  the 
slide-valve,  inclosed  in  a  steam-chest,  and  moved  by  the 
valve-rod,  R.  The  slide-valve  covers  the  exhaust-port,  N, 
and  one  of  the  other  two  ports,  A  and  B. 

(a)  Steam  from  the  boiler  enters  the  steam-chest  at  M.     When 
the  valve  is  in  position,  as  shown  in  Fig.  231,  "  live  "  steam  passes 
through    the    induction-port,   A, 

into  the  cylinder,  and  pushes  the 
piston,  as  indicated  by  the  arrows, 
forcing  out  the  "  dead "  or  ex- 
haust steam  by  the  eduction- 
port,  B,  and  the  exhaust-port,  N. 
As  the  piston  nears  the  end  of  its 
journey  in  this  direction,  the  valve-  f\  M 
rod,  R,  is  moved  by  an  "eccen-  £ 
trie,"  or  other  device,  and  shifts 
the  valve  into  position,  as  shown 
in  Fig.  232.  This  movement  of 
the  slide-valve  changes  B  to  an 
induction-port,  by  which  "live" 
steam  is  admitted  to  the  other 
face  of  the  piston,  pressing  it  in 

the  direction  indicated  by  the  arrow,  and  forcing  the  "  dead  "  steam 
out  through  A  and  N.  Then  the  slide-valve  is  pushed  back  to  its 
former  position  by  the  rod,  R.  and  the  alternating  movement  of  the 
piston  thus  continued.  The  piston-rod  and  the  valve-rod  work  through 
steam-tight  packing  boxes. 

(b)  The  outer  end  of  the  piston-rod  carries  a  transverse  bar  or 
cross-head  that  slides  between  two  guide-bars,  so  that  the  motion  of 
the  piston-rod  is  always  along  the  axis  of  the  cylinder.     The  same 


FIG.  232. 


310  SCHOOL  PHYSICS. 

end  of  the  piston-rod  is  pivoted  to  a  pitman  or  connecting-rod,  the 
other  end  of  which  is  attached  to  a  crank  on  the  shaft.  The  pitman 
receives  the  reciprocating  motion  of  the  piston-rod,  and  imparts  a 
rotary  motion  to  the  crank-shaft.  This  shaft  carries  a  heavy  fly- 
wheel, the  accumulated  energy  of  which  carries  the  shaft  across  the 
two  "  dead-points  "  when  the  piston  is  at  one  end  or  the  other  of  the 
cylinder.  The  fly-wheel  otherwise  tends  to  steadiness  of  motion,  and 
often  serves  as  a  belt-pulley.  In  large  engines,  the  length  of  the 
cylinder  is  generally  horizontal. 

(c)  When  the  exhaust  steam  escapes  through  N  into  the  air,  the 
engine  is  said  to  be  a  "high-pressure  "  or  a  "non-condensing"  engine; 
when  it  is  led  to  a  chamber  and  there  condensed  by  a  spray  of  cold 
water  for  the  purpose  of  removing  the  back  pressure  of  the  atmos- 
phere, the  engine  is  said  to  be  a  "low-pressure"  or  a  "condensing" 
engine.      As  the   water   is   pumped   from   the   condenser,  a  partial 
vacuum  is  maintained.     Sometimes  the  engine  expands  its  steam  in 
two,  three,  or  four  successive  stages,  and  in  two,  three,  or  four  distinct 
cylinders,  the  first  taking  steam  directly  from   the   boiler,  and  the 
others  taking  it  from  the  exhaust-port  of  the  cylinder  working  at 
the  next   higher   pressure.      Such    engines    are    called   respectively, 
"double-expansion,"  "triple-expansion,"  and  "quadruple-expansion" 
engines.     The  live  steam  may  be  cut  off  from  the  cylinder  during  the 
latter  part  of  the  travel  of  the  piston,  leaving  the  steam  in  the  cylin- 
der to  expand  with  decreasing  pressure  to  the  end  of  the  stroke.     The 
point  of  "  cut-off  "  may  be  fixed,  as  at  three-fourths  of  the  stroke,  or  it 
may  be  variable  with  the  nature  of  the  work.     In  the  latter  case,  the 
cut-off  device  may  be  adjusted  automatically. 

(d)  More  heat  is  carried  to  the  cylinder  of  a  steam-engine  than  is 
carried  from  it.     The  piston  does  work  at  every  stroke,  and  every 
stroke  annihilates  heat.     With  a  given  supply  of  steam,  the  engine 
will  give  out  less  heat  when  it  is  made  to  labor  than  when  it  runs 
light. 

(«)  With  all  of  its  merits  and  all  of  its  improvements,  the  modern 
steam-engine  utilizes  less  than  15  per  cent  of  the  heat  energy  devel- 
oped by  the  combustion  of  the  fuel. 

(y*)  Good  steam-engines  are  now  easily  accessible  from  nearly  every 
school,  and  should  be  studied  in  detail,  and  by  direct  inspection. 
The  action  of  the  pitman,  the  crank,  the  crank-shaft,  the  fly-wheel, 
and  the  dead-points  may  be  illustrated  by  almost  any  sewing- 
machine. 


THE   RELATION  BETWEEN   HEAT   AND    WORK.       311 


CLASSROOM  EXERCISES. 

1.  Show  that  the  high  latent  heat  of  water  has  an  important  rela- 
tion to  the  fact  that  when  the  temperature  of  the  atmosphere  rises 
above  0°,  all  the  ice  and  snow  of  winter  do  not  melt  in  a  single  day. 

2.  If  a  cannon  ball  weighing  192.96  pounds,  and  moving  with  a 
velocity  of  2,000  feet  per  second,  could  be  suddenly  stopped  and  all  its 
kinetic  energy  converted  into  heat,  to  what  temperature  would  that 
heat  warm  100  pounds  of  ice-cold  water  ? 

Solution :  —  K.E.  =  f^  =  192.96  x2000«=  12j000)000) the number of 

'£g  oi.oz 

foot-pounds.  Division  of  the  number  of  foot-ponnds  by  778  gives  the 
number  of  heat-units  (pound-Fahrenheit)  developed.  This  number 
divided  by  100  gives  the  number  of  heat-units  for  each  pound  of  the 
water,  and  consequently  the  number  of  Fahrenheit  degrees  that  it  will 
raise  the  temperature.  This,  added  to  32°,  the  initial  temperature, 
will  give  the  temperature  called  for. 

3.  A  steam-engine  raises  8,540  Kg.  to  a  height  of  50  m.     How 
many  calories  are  thus  expended  ? 

4.  One  gram  of  hydrogen  is  burned  in  oxygen.     To  what  tempera- 
ture would  a  kilogram  of  water  at  0°  be  raised  by  the  combustion  ? 

5.  From  what  height  must  a  block  of  ice  at  0°  fall  that  the  heat 
generated  by  its  collision  with  the  earth  would  just  melt  it  if  all  of 
the  heat  was  utilized  for  that  purpose  ? 

6.  Show  that  to  raise  the  temperature  of  a  pound  of  iron  from  0° 
to  100°  requires  more  energy  than  to  raise  7  tons  of  iron  a  foot  high. 

7.  To  what  height  cpuld  a  ton  weight  be  raised  by  utilizing  all 
the  heat  produced  by  burning  5  pounds  of  pure  carbon  ? 

Ans.  28,280  feet. 

8.  Find  the  height  to  which  it  could  be  raised  if  the  coal  had 
the  following  percentage  composition  :  — 

carbon,  88.42 ;  hydrogen,  5.61 ;  oxygen,  5.97. 

9.  With  what  velocity  must  a  leaden  bullet  strike  a  target  that  its 
temperature 'may  be  raised  100°  by  the  collision,  supposing   all  its 
energy  of  motion  to  be  spent  in  heating  the  bullet  ?     (Specific  heat  of 
lead,  0.0314;  </ =  980  cm.) 

10.  The  specific  heat  of  tin  is  .056  and  its  latent  heat  of  fusion  is 
25.6  Fahrenheit   degrees.     Find  the   mechanical  equivalent  of  the 
amount  of  heat  needed  to  heat  6  pounds  of  tin  from  374°  F.  to  its 
melting  point,  442°  F.,  and  to  melt  it. 


CHAPTER  V. 
RADIANT   ENERGY:    ETHER   PHYSICS. 

I.    NATURE   OF   RADIATION. 

254.  The  Ether.  —  Physicists  are  generally  of  the  opin- 
ion that  all  space  is  filled  with  an  incompressible  medium 
of  extreme  tenuity  and  elasticity.      TJiis  hypothetical  me- 
dium is  called  the  ether.     The  variety  of  the  phenomena 
for  which  the  ether  hypothesis  offers  the  only  explanation 
that  modern  science  can  accept  (see  §  10)  is  so  great  that 
the  unproved  existence   of   the  ether  is   confidently   ac- 
cepted. 

(a)  It  has  been  estimated  that  the  density  of  the  ether  is  9.36 
x  10~19,  which  is  enormously  great  as  compared  with  that  which  air 
would  assume  in  interstellar  space.  It  has  been  estimated  that  its 
rigidity  is  about  0.000,000,001  that  of  steel,  so  that  masses  of  ordinary 
matter  readily  pass  through  it.  Its  structure  is  assumed  to  be  con- 
tinuous instead  of  granular  like  that  of  ordinary  matter  (see  §  3). 
It  is  regarded  as  an  incompressible  substance  pervading  all  space  and 
penetrating  between  the  molecules  of  all  ordinary  matter  wh^ch  are 
embedded  in  it  and  connected  with  one  another  by  its  means.  It  has 
been  compared  to  an  impalpable  and  all-pervading  jelly  through 
which  the  particles  of  ordinary  matter  move  freely ;  through  which 
heat  arid  light  waves  are  constantly  throbbing ;  which  is  constantly 
being  set  in  local  strains  and  released  from  them,  and  being  whirled 
in  local  vortices,  thus  producing  the  various  phenomena  of  electricity 
and  magnetism. 

255.  Radiant  Energy. — Since  the  ether  fills  all  inter- 
molecular  spaces,  it  follows  that  the  vibrating  molecules 

312 


NATURE   OF   RADIATION.  313 

of  a  body  must  communicate  their  motion  to  it.  The 
periodic  disturbances  thus  communicated  to  the  ether  are 
propagated  through  it  in  the  form  of  waves  that  are 
assumed  to  be  transverse,  and  with  a  velocity  of  about 
186,000  miles  per  second.  Conversely,  when  these  ether- 
disturbances  reach  a  body,  they  may  communicate  their 
energy  to  the  molecules  of  that  body,  and  thus  increase 
the  total  energy  of  that  body.  The  transference  of  energy 
by  means  of  periodic  disturbances  in  the  ether  (without  re- 
gard to  the  precise  nature  of  those  disturbances)  is  called 
radiation.  The  energy  thus  transferred  is  called  radiant 
energy. 

(a)  The  mechanism  of  radiation  involves  two  correlative  processes, 
emission  and  absorption,  the  former  term  referring  to  the  communi- 
cation of  disturbances  to  the  ether,  and  the  latter  to  the  reception  of 
disturbances  from  the  ether.     Any  increase  in  the  vibratory  molecular 
energy  of  a  body  increases  its  total  radiation.     Any  increase  in  the 
rapidity  of  those  molecular  vibrations  correspondingly  increases  the 
number  of  the  ether  disturbances  in  a  unit  of  time,  i.e.,  increases 
the  wave-frequency.     There  is,  therefore,  an  evident  analogy  between 
the  phenomena  of  radiation  and  those  of  sound. 

(b)  The  energy  of  radiation  is  measured  by  totally  absorbing  it 
and  determining  the  heating  effect  produced  by  it.    Lampblack  is  the 
most  efficient  substance  known  for  such  absorption. 

256.  A  Ray  is  a  line  along  which  radiant  energy  is  prop- 
agated ;  i.e.,  the  straight  line  perpendicular  to  the  wave- 
front.  A  collection  of  parallel  rays  is  called  a  beam.  A 
collection  of  converging  or  diverging  rays  is  called  a 
pencil. 

(a)  The  expressions,  rays,  beams,  and  pencils,  are  traces  of  an 
exploded  theory.  So  far  as  they  pertain  to  the  wave  theory,  they 
are  merely  convenient  geometrical  conceptions,  having  no  material 
existence. 


314  SCHOOL  PHYSICS. 

257.  Incident  Radiation  may  be  transmitted,  reflected 
or  absorbed  by  the  body  upon  which  it  falls.     When  a 
body  absorbs  radiant  energy,  it  is  heated  thereby. 

Experiment  203.  —  Take  a  white-hot  poker  into  a  dark  room.  You 
are  conscious  of  the  sensations  of  heat  and  light,  and  readily  attribute 
both  sensations  to  the  energy  radiated  by  the  poker  ;  i.e.,  you  say  that 
the  poker  emits  heat  and  white  light.  The  light  gradually  becomes 
reddish,  and  finally  fades  from  view.  There  is  a  continuous  change 
from  the  emission  of  white  light  and  much  heat  to  that  of  no  light 
and  less  heat. 

258.  Radiant  Energy  is  Recognized  by  its  phenomena, 
which  may  be  classified  as  luminous,  thermal,  and  chem- 
ical. 

(a)  Not  even  in  theory  can  we  assign  limits  to  the  length  of  the 
ether  undulations.  Some  of  these  waves  are  competent  to  excite  the 
optic  nerve  and  to  produce  vision  ;  some  are  not.  This  ability  and 
inability  are  matters  of  wave-length.  The  variety  of  the  effects  must 
not  be  permitted  to  obscure  the  identity  of  the  cause.  All  of  these 
ether  vibrations  are  of  the  same  nature.  Most  of  the  properties  and 
phenomena  of  radiant  energy  are  most  conveniently  studied  by 
luminous  effects,  which  constitute  the  chief  subject-matter  of  this 
chapter. 


II.    LIGHT:     VELOCITY   AND   INTENSITY. 

259.  Light.  —  The  portion  of  radiant  energy  that  is 
capable  of  producing  the  effect  of  vision  constitutes  light. 

(a)  The  longest  recognized  ether  wave  is  3,000  x  10~6  cm. ;  the 
shortest  is  18.5  x  10~6  cm.  These  wave-lengths  correspond  respectively 
to  vibration  frequencies  of  10  x  1012  and  1,622  x  1012.  The  radiant 
energy  that  constitutes  light  lies  within  the  comparatively  narrow 
limits  of  7.6  x  10~6  cm.,  and  3.9  x  10~5  cm.,  wave-lengths  that  respec- 
tively correspond  to  vibration-frequencies  of  392  x  1012  and  757  x  1012. 


LIGHT:   VELOCITY  AND   INTENSITY.  315 

While  the  total  range  already  observed  is  more  than  seven  octaves, 
the  range  within  the  limits  that  correspond  to  light  is  little  more 
than  one  octave. 

260.  Visible  Bodies  are  visible  because  of  the  light  that 
they  send  to  the  eye  of  the  observer.  This  is  true  whether 
the  body  shines  by  its  own  or  another's  light,  i.e.,  whether 
it  is  self-luminous  like  a  "  live  "  coal,  or  illuminated  like  a 
"  dead  "  coal. 

(a)  Light  makes  luminous  bodies  visible  but  is  itself  invisible. 
The  illumination  of  the  path  of  a  sunbeam  entering  a  darkened  room 
is  due  to  the  reflection  of  light  by  the  dust  motes  floating  in  the  air. 
When  a  sunbeam  is  sent  through  moteless  air,  its  path  is  imper- 
ceptible. 

XOTE.  —  For  many  experiments  in  light,  a  darkened  room  is  desir- 
able. The  windows  should  be  provided  with  opaque  curtains  so 
arranged  that  the  sunlight  may  be  quickly  and  completely  excluded 
from  the  classroom  and  laboratory. 

Rectilinear  Propagation. 

Experiment  204.  —  Provide  six  blocks  H  x  2|  x  3^  inches,  and  three 
other  pieces  of  wood  each  }  x  3|  x  4  inches.  Place  three  postal  cards 
one  over  the  other  on  a  board  and  perforate  them  with  a  stout  needle 
about  half  an  inch  below  the  middle  of  one  end.  Pare  off  the  rough 
edges  of  the  holes  with  a  sharp  knife,  and  again  pass  the  needle 
through  each  hole  to  make  its  edge  smooth  and  even.  From  these 
materials,  make  three  screens  like  that  shown  at  A  or  B  in  Fig.  242. 
Place  the  three  screens  parallel  to  each  other  and  with  their  blocks 
separated  by  two  of  the  other  blocks.  Pass  a  thread  through  the  holes 
in  the  screens  and  carefully  put  it  under  tension  to  be  sure  that  the 
perforations  are  in  a  straight  line.  If  necessary,  adjust  the  screens 
for  that  purpose.  Remove  the  thread  without  disturbing  the  adjust- 
ment. On  the  remaining  block,  place  a  lighted  candle  of  such  length 
that  its  flame  is  at  the  height  of  the  perforations  in  the  cards.  Place 
eye  and  candle  so  that  the  flame  may  be  seen  through  the  screen  per- 
forations. Move  one  of  the  screens  a  little  so  that  the  three  holes 
are  not  in  a  straight  line ;  the  candle  flame  cannot  be  seen  as  it  was 
before. 


316  SCHOOL   PHYSICS. 

261.  Radiant  Energy  is  Propagated  along  straight  lines 
when  the  medium  is  homogeneous,  i.e.,  when  it  has  a  uniform 
composition  and  density. 

(a)  The  familiar  experiment  of  "  taking  sight "  depends  upon 
this  fact,  for  \ve  see  objects  by  the  light  that  they  send  to  the  eye. 
A  small  beam  of  light  that  enters  a  darkened  room  illuminates  a 
straight  path.  The  use  of  fire-screens  and  sunshades  illustrates  the 
same  fact. 

262.  Transparency,  etc.  —  According  to  the  freedom  with 
which   they  transmit  light,   bodies  are   classified  as   trans- 
parent, translucent,  and  opaque.     Transparent  bodies,  as 
glass,  transmit  light  so  freely  that  objects  may  be  seen 
through  them  distinctly.      Translucent  bodies,   as    oiled 
paper,    transmit   light   so   imperfectly  that   objects  seen 
through  them  appear  indistinct.     Opaque  bodies  cut  off 
the  light  entirely,  and  prevent  objects  from  being  seen 
through   them   at  all.      No  sharp  line  of  separation  can 
be  drawn  between  these  classes. 

(a)  When  light  falls  upon  a  mass  of  small  particles  or  thin  films 
of  substances  that  are  usually  transparent,  as  finely-pounded  glass  or 
ice,  or  froth,  or  foam,  or  cloud,  most  of  the  light  is  reflected.  What 
passes  through  one  particle  or  film  is  reflected  by  another.  Such 
masses  are  brilliantly  white  in  sunlight.  As  the  light  is  reflected  and 
not  transmitted,  such  masses  are  opaque. 

Shadows. 

Experiment  205.  —  Hold  a  lead  pencil  between  the  flame  of  an  ordi- 
nary lamp  and  a  sheet  of  paper  about  two  feet  distant  from  the  lamp, 
first  with  the  edge  of  the  flame  toward  the  pencil,  and  then  with  the 
side  of  the  flame  toward  the  pencil.  Notice  the  difference  in  the 
appearance  of  the  screen. 

Experiment  206.  —  Coat  with  asphaltum  varnish  the  lower  half  of 
the  outer  surface  of  the  chimney  of  a  lamp  that  has  a  large  flat  flame. 


LIGHT:   VELOCITY   AND   INTENSITY. 


317 


At  the  height  of  the  flame,  scrape  the  varnish  from  a  spot  3  or  4  mm. 
in  diameter.  Place  the  chimney  on  the  lighted  lamp  with  the  clear 
spot  opposite  the  middle  of  a  screen  of  light-colored  paper  and  about 
2  in.  from  it.  Instead  of  being  varnished,  the  chimney  may  be 
smoked,  or  a  sheet  of  cardboard  may  be  rolled  into  a  hollow  cylinder 
large  enough  to  surround  the  lamp;  a  hole  may  be  cut  in  the  card- 
board at  the  proper  height.  Hang  a  croquet  ball  midway  between  the 
lamp  and  the  screen.  If  the  room  is  not  darkened,  place  the  ball  and 
the  screen  between 
the  lamp  and  the 
window.  Prick  a  pin- 
hole  through  the 
darkened  section  of 
the  screen  and  look 
through  it  toward 
the  lamp.  From  the 
further  side  of  the  FIG.  233. 

screen,  prick  a  series 

of  such  holes  about  an  inch  apart  and  in  a  straight  line,  looking 
through  each  hole  before  another  is  pricked.  When  you  have  pricked 
a  hole  through  w7hich  you  can  see  the  luminous  spot  on  the  lamp- 
chimney,  examine  the  other  side  of  the  screen  and  notice  that  the  pin- 
hole  is  outside  the  darkened  section. 

Experiment  207.  —  Replace  the  chimney  used  in  Experiment  206 
by  one  that  is  clear,  and  see  that  the  side  of  the  flame  is  turned 
toward  the  ball.  Examine  the  darkened  section  on  the  screen 

i 


FIG.  234. 


and  notice  that  its  central  disk  is  equally  dark  in  all  its  parts, 
and  surrounded  by  a  ring  of  varying  darkness.  Beginning  at  the 
middle  of  the  disk,  prick  pin-holes  as  before,  examining  each  in  suc- 
cession, and  avoiding  those  pricked  in  Experiment  206.  Notice  that 


318  SCHOOL  PHYSICS. 

you  cannot  see  the  flame  through  any  hole  in  the  central  disk,  that 
you  can  see  part  of  the  flame  through  any  hole  in  the  annular  space, 
and  that  you  can  see  the  whole  of  the  flame  through  any  hole  outside 
the  annular  space. 

263,  A  Shadow  is  the  darkened  space  from  which  an 
opaque  body  cuts  off  light.     If  the  source  of  light  has  con- 
siderable magnitude  there  will  be  a  region  of  complete 
shadow,  called  the  umbra,  surrounded  by  a  partial  shadow, 
called  the  penumbra.     No  light  enters  the  umbra ;    the 
penumbra  receives  light  from    a   part   of   the   luminous 
surface. 

264.  An  Image  is  an  optical  counterpart  of  an  object  and 
may  be  formed  by  passing  light  through  a  small  aperture, 
by  reflecting  it  with  a  mirror,  or  by  refracting  it  with  a 
lens.     When  the  light  actually  comes  from  the  image  to 
the  eye,  the  image  is  real.     Such  an  image  may  be  re- 
ceived on  a  screen.     When  the  light  seems  to  come  from 
the  image  to  the  eye  but  does  not,  the  image  is  virtual. 
All  virtual  images  are  optical  illusions. 

Inverted  Images. 

Experiment  208.  —  Place  the  opened  end  of  an  empty  tin  fruit-can 
upon  a  hot  stove  and  leave  it  there  just  long  enough  to  melt  off  the 
mutilated  cover.  Make  a  good  sized  nail-hole  at  the  center  of  the  other 
end.  Cover  the  nail-hole  with  tin-foil,  anu  the  other  end  of  the  can 
with  thin  tracing  cloth  or  paper.  Prick  a  pin-hole  in  the  tin-foil,  and 
turn  it  toward  a  candle  flame.  Upon  the  paper  may  be  seen  an  in- 
verted image  the  size  of  which  will  depend  upon  the  distance  of  the 
flame  from  the  pin-hole.  The  image  will  be  seen  more  plainly  if  the 
room  is  darkened,  or  a  dark  cloth  used  (after  the  manner  of  a  pho- 
tographer) to  shut  the  outside  light  from  the  eyes  and  the  screen. 

Experiment  209.  —  Bore  a  hole  about  3  cm.  in  diameter  in  the  side 
of  a  wooden  box,  paste  or  tack  tin-foil  over  the  hole,  and  prick  the 


UHIVERS1TY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSICS 
LIGHT  :    VELOCITY   AND   INTENSITY.  319 

tin-foil  with  a  pin.  Invert  the  box  over  a  lighted  candle  of  such 
height  that  its  flame  will  be  at  the  level  of  the  pin-hole.  The  box 
should  be  so  large  that  the  candle  cannot  set  it  on  fire.  Darken  the 
room,  and  hold  a  paper  screen  before  the  hole  in  the  tin-foil.  Move 
the  screen  backward  and  forward  and  notice  that,  in  any  position,  the 
length  of  the  flame  is  to  the  length  of  the  image  of  the  flame  as  the 
distance  from  the  pin-hole  to  the  flame  is  to  the  distance  from  the  pin- 
hole  to  the  image.  Replace  the  tin-foil  by  another  piece  from  which 
has  been  cut  a  triangle  1  or  2  mm.  on  a  side.  Notice  that  the  change 
in  the  shape  of  the  aperture  does  not  make  much  difference  with  the 
form  of  the  image.  Replace  this  tin-foil  by  another  piece  from  which 
has  been  cut  a  triangle  about  2  cm.  on  a  side.  Notice  that  the  image 
is  brighter  and  that  its  outline  is  less  distinct. 

265.  Images  by  Apertures.  —  If  light  from  a  highly 
luminous  body  is  admitted  to  a  darkened  room  through 
a  small  hole  in  the  shutter  and  there  received  upon  a 
white  screen,  it  will  form  an  inverted  image  of  the  object. 


FIG.  235. 

As  the  rays  are  straight  lines,  they  cross  at  the  aper- 
ture ;  hence,  the  inversion  of  the  image.  The  darkened 
room  constitutes  a  camera  obscura  of  simple  form.  The 
image  of  the  school  playground  at  recess  is  very  interest- 
ing, and  is  easily  produced. 

(a)  When  the  aperture  is  circular,  each  point  of  the  luminous  sur- 
face sends  a  cone  of  rays  to  the  screen,  and  illuminates  a  circular  spot 


320  SCHOOL   PHYSICS. 

upon  it.  When  the  aperture  is  triangular,  or  square,  each  point  sends 
a  pyramid  of  rays,  and  illuminates  a  triangular  or  a  square  spot.  In  any 
case,  there  will  be  an  image  of  the  aperture  thrown  upon  the  screen 
for  every  point  in  the  luminous  surface.  As  these  superposed  images 
of  the  aperture  are  symmetrically  placed  with  reference  to  the  corres- 
ponding points  of  the  luminous  surface,  and  as  they  overlap  each  other, 
they  build  up  an  image  of  the  luminous  body  regardless  of  the  shape 
of  the  aperture.  The  idea  may  be  more  easily  comprehended  by 
imagining  the  building  up  of  a  star-shaped  figure  by  using  small, 
round  wafers.  The  smaller  the  wafers,  the  sharper  the  outline  of  the 
star.  Remembering  that  the  size  and  shape  of  our  analogic  wafer 
depend  upon  the  size  and  shape  of  the  aperture,  it  ought  not  to  be 
difficult  to  understand  the  phenomena  presented  by  images  like  those 
now  under  consideration.  The  aperture  or  the  wafer  may  be  so  large 
as  to  destroy  all  resemblance  between  the  image  and  the  luminous 
object,  and  to  substitute  therefor  a  resemblance  to  the  aperture  or 
wafer  itself. 

266.  The  Velocity  of  Light  is  about  186,000  miles 
(3  x  1010  cm.)  per  second.  For  terrestrial  distances,  the 
passage  of  light  is,  therefore,  practically  instantaneous. 

(a)  At  equal  intervals  of  42  h.  28  min.  36  s.,  the  nearest  of  Jupiter's 
satellites  passes  within  his  shadow  and  is  thus  eclipsed.  This  phe- 
nomenon would  be 
seen  from  the 
earth  at  equal  in- 
tervals if  light  trav- 
eled instantane- 
ously from  planet 

FIG.  236.  to  Planet    In  1675> 

a  Danish  astron- 
omer noticed  that  the  interval  between  successive  eclipses  as  ob- 
served was  longer  during  the  half  year  when  the  earth  was  passing 
from  conjunction  to  opposition,  as  from  E  to  E',  than  it  was  when  the 
earth  was  passing  over  the  other  half  of  its  orbit,  as  from  E'  to  E. 
If,  when  the  earth  was  at  E,  the  time  of  successive  eclipses  was  com- 
puted a  year  in  advance,  the  eclipse  observed  six  months  later  when 
the  earth  was  at  E',  seemed  to  be  16  min.  36  sec.  behind  time,  the  time 
apparently  lost  being  regained  in  the  next  six  months.  This  led  irre- 


LIGHT  :    VELOCITY    AND   INTENSITY. 


321 


sistibly  to  the  conclusion  that  it  requires  16  inin.  36  sec.  for  light  to 
pass  over  the  diameter  of  the  earth's  orbit  from  E  to  E'.  This  dis- 
tance being  approximately  known,  the  velocity  of  light  is  easily  com- 
puted. The  velocity  of  light  has  been  measured  by  other  means, 
giving  results  that  agree  substantially  with  that  above  recorded. 

Intensity  of  Illumination. 

Experiment  210. — Make  three  cardboard  screens,  A,  £,  and  C, 
respectively  5  cm.,  12  cm.  and  17  cm.  on  a  side.  Draw  a  line  parallel 
to  each  edge  of  B  and  C,  and  at  a  distance  of  1  cm.  therefrom,  thus 
inscribing  squares  10  cm.  and  15  cm.  on  a  side.  Divide  the  smaller  in- 
scribed square  into  four  squares,  each  the  size  of  -4,  and  the  larger 
inscribed  square  into  nine  such  squares.  Mount  the  three  screens  so 


FIG.  237. 

that  they  stand  upright  with  their  middle  points  at  the  height  of  the 
cleared  spot  on  the  lamp-chimney  used  in  Experiment  206.  Instead 
of  the  asphaltum  coat  on  the  lamp-chimney,  a  perforated  cardboard 
screen  may  be  used  as  sl/own  in  Fig.  237.  The  screens  may  be  con- 
veniently supported  by  soft-wood  rods,  each  having  a  fine  slit  sawed 
in  one  end  and  a  sewing-needle  thrust  half-way  into  the  other  end. 
Place  A  about  30  cm.  from  the  perforation.  Set  C,  parallel  to  A  and 
at  such  a  distance  that  the  shadow  of  A  just  covers  its  nine  squares. 
Then  place  B  so  that  the  shadow  of  A  just  covers  its  four  squares. 
Determine  the  relative  distances  of  A,  B,  and  C  from  the  source  of 
light.  Remove  A  and  notice  that  the  light  that  previously  fell  upon 
it  now  falls  upon  B.  Remove  the  second  screen  and  notice  that  the 
light  that  previously  fell  upon  A  and  B  now  falls  upon  C. 

267.    The  Intensity  of  Radiation  that  falls  upon  a  sur- 
face — 

21 


322 


SCHOOL  PHYSICS. 


(1)  Varies  inversely  as  the  square  of  the  distance  betiveen 
this  surface  and  the  source  of  radiation. 

(2)  Varies  with  the  angle  that  the  incident  radiation  makes 
with  this  surface,  being  at  a  maximum  when  the  surface  is 
perpendicular  to  the  direction  of  propagation. 

(a)  In  Experiment  210,  the  light  that  fell  upon  A  was  diffused 
over  four  times  the  area  at  B,  at  twice  the  distance ;  and  nine  times 
the  area  at  C,  at  three  times  the  distance.  With  the  same  quantity 
of  light  diffused  over  nine  times  the  area,  the  intensity  of  the  illumi- 
nation, i.e.,  the  quantity  of  light  per  unit  of  surface,  is  only  1  as  great. 

Photometry. 

Experiment  an.  —  Arrange  apparatus  in  a  darkened  room  as  shown 
in  Fig.  238,  where  S  represents  a  screen  of  white  paper  or  cardboard, 
and  jR,  a  small  rod  placed  upright  a  few  inches  from  S  (a  cheap  pen 
and  pen-holder,  or  a  lead  pencil  held  by  a  bit  of  wax  on  the  table  will 
answer).  The  two  flames  should  be  on  opposite  sides  of  a  plane  per- 
pendicular to  the  screen  and  passing  through  R,  and  at  equal  angular 
distances  from  it ;  they  should  be  at  the  same  level,  and  the  flat  lamp- 


FIG.  238. 

wick  should  stand  diagonally  to  the  screen.  Place  C  about  20  inches 
from  S,  and  move  L  until  the  two  shadows  upon  S  nearly  touch  and 
are  of  equal  darkness.  The  candle  and  the  lamp  are  now  throwing 
equal  amounts  of  light  upon  the  screen.  If  the  distance  from  S  to 
L  is  twice  that  from  £  to  C,  then  L  is  four  times  as  powerful  a  light 
as  C ;  if  the  distance  is  three  times  as  far,  L  is  nine  times  as  powerful. 
Apparatus  thus  used  constitutes  a  Rnmford  photometer. 


LIGHT  :    VELOCITY   AND   INTENSITY.          .         323 

Experiment  212.  —  Drop  some  melted  paraffine  upon  a  piece  of 
heavy,  unglazed  white  paper,  making  a  spot  about  an  inch  in  diameter. 
Remove  the  excess  of  paraffine  with  a  knife,  and  heat  the  spot  with  a 
flat-iron  or  can  of  water.  Support  the  paper  as  a  vertical  screen. 
When  the  paraffined  disk  is  viewed  by  transmitted  light,  it  appears 
brighter  than  the  surrounding  paper ;  when  viewed  by  reflected  light, 
it  appears  darker.  Place  a  lighted  standard  candle  (see  §  268)  at  one 
end  of  a  table,  and  a  lamp  or  gas-flame  at  the  other  end.  Place 
the  screen  between  them,  and  arrange  the  pieces  so  that  the  middle 
points  of  the  candle  flame,  the  translucent  disk,  and  the  lamp-flame 
are  in  a  straight  line  that  is  perpendicular  to  the  screen.  If  the  lamp- 
flame  is  flat,  set  it  diagonally  to  the  screen.  Move  the  screen  along 
the  line  between  the  candle  and  the  lamp  until  its  two  sides  are 
equally  illuminated  ;  i.e.,  until  the  paraffined  spot  is  invisible,  or  until 
the  contrast  between  it  and  the  rest  of  the  screen  is  the  same  on  both 
sides  when  viewed  at  the  same  angle.  Find  the  ratio  between  the 
distances  of  candle  and  lamp  from  the  screen,  and  square  the  ratio  to 
find  the  candle-power  of  the  lamp.  Apparatus  thus  used  constitutes  a 
Bunsen  photometer. 

268.  Photometry  is  the  measurement  of  the  relative 
amounts  of  light  emitted  by  different  sources.  The  usual 
process  is  to  determine  the  relative  distances  at  which 
two  sources  of  light  produce  equal  intensities  of  illumina- 
tion. The  standard  in  general  use  is  the  light  given  by  a 
sperm  candle  (of  the  size  known  as  "  sixes  ")  when  burn- 
ing 120  grains  per  hour.  The  result  is  expressed  by  say- 
ing that  the  light  tested  has  so  many  candle-power. 

CLASSROOM  EXERCISES. 

1.  Describe  the  shadow  cast  by  a  wooden  ball  (a)  when  the  source 
of  light  is  a  luminous  point ;  (6)  when  the  source  of  light  is  a  white- 
hot  iron  ball  smaller  than  the  wooden  ball;  (c)  when  it  is  of  the  same 
size  ;  (e?)  when  it  is  larger. 

2.  Do  sound  waves  or  water  waves  the  more  closely  resemble  waves 
of  light?    Why? 

3.  State  clearly  your  idea  of  the  carrier  of  radiant  energy. 


324  SCHOOL   PHYSICS. 

4.  Explain  the  formation  of  inverted  images  by  small  apertures. 

5.  Draw  figures  to  illustrate  the  effect  that  doubling  the  distance 
of  an  opaque  body  from  a  source  of  light  has  upon  the  shadow  of  the 
former. 

6.  A  coin  is  held  5  feet  from  a  wall  and  parallel  to  it.    A  luminous 
point,  15  inches  from  the  coin,  throws  a  shadow  of  it  upon  the  wall. 
How  does  the  size  of  the  shadow  compare  with  that  of  the  coin  ? 

7.  An  opaque  screen,  3  inches  square,  is  held  12  inches  in  front  of 
one  eye ;  the  other  eye  is  shut ;   the  screen  is  parallel  with  a  wall 
100  feet  distant.     What  area  on  the  wall  may  be  concealed  by  the 
screen  ? 

8.  A  standard  candle  is  2  feet  and  a  lamp  is  6  feet  from  a  wall. 
The  shadows  on  the  wall  are  of  equal  intensity.     What  is  the  candle- 
power  of  the  lamp  V 

9.  An  electric  arc  lamp  100  feet  north  of  me  and  one  200  feet  south 
of  me  illuminate  opposite  sides  of  a  sheet  of  paper  in  my  hand  and 
render  invisible  a  grease  spot  on  the  paper.     How  do  the  illuminating 
powers  of  the  lamps  compare  ? 

10.  If  you  hold  a  sheet  of  paper  with  a  greased  spot  on  it  between 
you  and  the  light,  the  spot  will  look  lighter  than  the  rest  of  the  sheet. 
Why  is  this  ? 

11.  If  you  hold  the  sheet  in  front  of  you  when  you  are  turned  away 
from  the  light,  the  spot  will  look  darker  than  the  rest  of  the  sheet. 
Why  is  this  ? 

12.  Study  the  shadows  cast  by  an  electric  arc  lamp,  and  write  a 
very  brief  description  of  the  penumbra  of  the  shadows. 

13.  Describe  the  shape  in  space  of  the  umbra  and  the  penumbra  of 
the  moon's  shadow.     Draw  an  illustrative  figure. 

14.  When   has   an   umbra  an  infinite  length,  and  when  a  finite 
length  ? 

15.  The  length  of  the  umbra  of  the  moon's  shadow  is  a  little  longer 
than  the  radius  of  the  moon's  orbit.     On  the  figure  drawn  for  Exercise 
13,  indicate  the  position  in  space  occupied  by  your  city  (a)  when  a 
total  eclipse  of  the  sun  is  visible  there ;  (b)  when  a  partial  eclipse  of 
the  sun  is  visible  there. 

16.  What  does  the  great  velocity  of  light  indicate  as  to  the  density 
and  the  elasticity  of  the  ether  ? 


LIGHT:    VELOCITY   AND   INTENSITY.  325 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  chalk-line;  a  standard  candle;  five 
"  Christmas"  candles ;  cardboard,  20  x  30  cm. ;  a  slender  wooden  rod ; 
two  small  kerosene  lamps ;  two  pieces  of  looking-glass,  10  cm.  square, 
tied  to  the  vertical  faces  of  two  rectangular  blocks. 

1.  Place  a  yardstick  vertically  against  the  wall  of  the  room.     Hold 
one  end  of  a  foot  rule  at  the  eye,  sight  along  the  upper  side  of  the  rule, 
and  bring  it  into  line  with  the  lower  end  of  the  yardstick.     Keeping 
the  rule  in  this  position,  hold  a  lead  pencil  vertically  across  its  further 
end  so  that  the  upper  end  of  the  pencil  is  in  line  with  the  upper  end 
of  the  yardstick.     Carefully  measure  the  length  of  the  part  of  the 
pencil  that  projects  above  the  rule,  and  compute  the  distance  of  your 
eye  from  the  yardstick. 

2.  From  a  point  on  a  blackboard  or  floor,  draw  two  lines  that 
diverge  1  inch  in  10  feet,  and  make  them  as  long  as  possible.     It  will 
be  convenient  to  use  a  chalked  line  for  this  purpose.     The  included 
angle  will  represent  (fairly  well)  the  angle  subtended  by  the  diam- 
eters of  the  moon  and  the  sun  as  observed  from  the  center  of  the 
earth.     "With  the  apex  of  the  angle  as  a  center,  draw  a  circle  4  inches 
in  diameter  to  represent  the  earth .     At  the  distance  of  10  feet,  draw 
a  circle  1  inch  in  diameter  to  represent  the  moon.     Imagine  the  long 
lines  extended  until  they  have  diverged  sufficiently  to  include  between 
them  a  circle  400  inches  in  diameter  to  represent  the  sun.     Compute 
the  distance  of  the  center  of  this  circle  from  the  apex  of  the  angle. 
Assume  the  diameter  of  the  earth  to  be  8,000  miles.     From  the  figure 
as  thus  completed  in  imagination,  compute  the  diameters  of  the  moon 
and  of  the  sun,  and  their  distances  from  the  earth.     Shade  the  tri- 
angular space  between  the  moon  and  the  center  of  the  earth.     Is  it 
possible  for  the  moon's  umbra  to  envelop  the  whole  earth  ?    Under  the 
assumed  conditions,  what  phenomenon  would  be  seen  by  an  observer 
looking  toward  the  inoon  from  the  portion  of  the  earth's  surface 
included  in  the  shaded  triangle?     By  an  observer  on  the  earth's 
surface  just  outside  that  shaded  part? 

3.  Arrange  a  Rumford  photometer  by  setting  up  a  rod  20  cm.  long 
and  1  cm.  in  diameter,  5  cm.  in  front  of  a  white  cardboard  screen 
20  cm.  tall  and  10  cm.  wide.     Mount  a  short  candle  upon  a  wooden 
block,  and  four  other  candles  of  the  same  kind  and  length  in  a  straight 
row  upon  another  block.     Place  the  block  with  the  single  candle  on 
one  side  of  the  median  plane,  and  the  block  with  the  four  candles 


326  SCHOOL  PHYSICS. 

on  the  other  side.  The  outside  candles  of  the  set  of  four  should  be 
equally  distant  from  the  rod.  After  the  candles  have  burned  for 
some  minutes,  carefully  trim  their  wicks  so  that  the  flames  shall  be  of 
the  same  size.  Stand  in  the  median  plane  and  so  adjust  the  distance 
of  the  single  candle  as  to  get  shadows  of  equal  intensity  as  described 
in  Experiment  211.  Measure  and  record  the  distances  of  the  two 
sources  of  light  from  the  screen  and  compare  the  result  with  the 
statements  of  §  267. 

4.  Instead  of  the  candles  of  Exercise  3,  use  two  small  kerosene 
lamps.     Place  them  at  equal  distances  from  the  rod,  and  turn  the 
edges  of  their  flames  toward  the  rod.     Turn  one  of  the  flames  down 
until  the  shadows  are  of  equal  darkness.     Turn  one  lamp  so  that  the 
side  of  its  flame  is  toward  the  rod.     Fix  the  attention  on  the  middle 
of  the  blurred  shadow.     If  the  two  shadows  are  of  equal  darkness, 
record  the  fact.     If  they  are  not,  move  one  of  the  lamps  until  they 
are.     Then  measure  and  record  the  distance  of  each  lamp  from  its 
shadow.     Record  your  conclusions  as  to  the  perfect  transparency  of  a 
lamp-flame. 

5.  Using  a  Bunsen  photometer,  compare  the  illumination  of  the 
four  candles  used  in  Exercise  3  with  that  of    a  standard   candle. 
Interchange  the   positions   of  the  lights,   and   record    the   average 
distances. 

6.  Place  two  plane  mirrors  so  that  an  observer  standing  in  the 
plane  of  the  screen  can  simultaneously  see  the  images  of  both  faces 
of  the  paraffined  spot,  and  compare  them  for  equality  of  illumination. 
Thus,  determine  the  candle-power  of  a  kerosene  lamp. 


III.    REFLECTION   OF   RADIANT   ENERGY. 

Experiment  213.  —  Paint  the  outside  of  a  pint  tin-pail  with  lamp- 
black, and  fill  the  vessel  with  hot  water.  Support  the  pail  a  few  inches 
above  the  table  and,  on  the  table  near  by,  lay  a  sheet  of  tin-plate.  Be- 
tween the  pail  and  the  sheet,  place  a  glass  or  wooden  screen  that  has 
an  aperture  about  2  cm.  in  diameter  so  that  radiant  energy  from  the 
pail  may  pass  through  the  aperture  and  fall  upon  the  tin  reflector 
on  the  table.  Place  one  bulb  of  a  differential  thermometer  so  that 
the  energy  radiated  directly  from  the  pail  will  be  cut  off  by  the  screen, 
while  that  reflected  by  the  sheet  of  tin,  in  accordance  with  the  law 


REFLECTION   OF   RADIANT   ENERGY. 


327 


FIG.   239. 


stated  in  §  76,  will  fall  upon  it.     Notice  the  effect  of  the  reflection. 
Move  the  bulb  out  of  the  line  of  reflection,  and  notice  the  effect. 

Experiment  214. — About  two  feet  from  an  air  thermometer,  place 
an  inverted  flower-pot.  Midway  between  the  two,  place  a  board  or 
glass  screen  that  reaches 
from  the  table  to  a  height 
of  several  inches  above  the 
bulb  of  the  air  thermometer. 
Upon  the  flower-pot,  place  a 
very  hot  brick.  Notice  that 
the  heat  of  the  brick  has 
little  effect  upon  the  ther- 
mometer. Then  hold  a  sheet 
of  tin-plate  over  the  screen  so 
that  energy  radiated  oblique- 
ly upward  from  the  brick 
may  be  reflected  obliquely  downward  toward  the  thermometer.  By 
properly  adjusting  the  position  of  the  reflector,  the  thermometer  may 
be  quickly  affected. 

269.  Reflection  of  Radiant  Energy  is  the  sending  back  of 
incident  ether  waves  by  the  surface  on  which  they  fall  into 
the  medium  from  which  they  come.  The  reflection  may  be 
irregular  or  regular. 

(a)  The  proportion  of  the  incident  energy  that  is  reflected  in- 
creases with  the  angle  o£  incidence  and  with  the  degree  of  polish  of 
the  reflecting  surface,  and  varies  according  to  the  nature  of  the 
reflecting  substance. 

NOTE.  —  The  laboratory  should  be  provided  with  a  porte-lumiere, 
which  consists  of  a  plane  mirror  so  mounted  and  fitted  with  adjust- 
ing appliances  that  the  direction  of  light  reflected  from  the  mirror 
may  be  easily  controlled.  The  mirror  is  placed  on  the  outside  of 
the  shutter  of  a  darkened  window  and  operated  from  within,  sunlight 
being  reflected  through  the  aperture  in  the  shutter. 

Experiment  215.  —  Let  a  beam  of  light  pass  through  an  opening  in 
the  shutter  of  a  darkened  room,  and  fall  upon  a  sheet  of  drawing 
paper  lying  on  the  table-top.  The  light  will  be  scattered,  and  will 
illuminate  the  room.  With  a  hand  mirror,  reflect  the  beam  down- 
ward into  a  tumbler  of  water  into  which  a  teaspoonful  of  milk  has  been 


328 


SCHOOL  PHYSICS. 


stirred.     The  milky  water  will  scatter  the  light,  and  illuminate  the 
room  as  if  it  was  self-luminous. 

270.    Irregular  Reflection  or  Diffusion  results  from  the 

incidence  of  radiant  energy 
upon  an  irregular  surface,  as  is 
illustrated  by  Fig.  240.  Bodies 
are  made  visible  to  the  eye 
mainly  by  the  light  that  they 
thus  diffuse. 


FIG.  Li.). 


Experiment  216.  —  Repeat  Experi- 
ment 215,  allowing  the  beam  of  light 
to  fall  upon  a  mirror  instead  of  drawing  paper.  Most  of  the  light 
will  be  reflected  in  a  definite  direction,  and  will  brilliantly  illuminate 
a  small  part  of  the  enclosing  wall.  Reflect  the  beam  downward 
into  a  tumbler  of  clear  water ;  the  tumbler  will  be  visible  but  the 
room  will  not  be  illuminated  as  it  was  by  the  milky  water. 

271.  Regular  Reflection  results  from  the  incidence  of 
radiant  energy  upon  a  polished  surface.  When  a  beam  of 
light  falls  upon  a  mirror,  the 
greater  part  of  it  is  reflected  in 
a  definite  direction  as  is  illus- 
trated by  Fig.  241,  and  forms 
an  image  of  the  object  from 
which  it  came.  A  perfect  mir- 
ror  would  be  invisible.  FIG.  241. 

Law  of  Reflection. 

Experiment  217.  —  Provide  a  semi-circular  table  like  that  shown  in 
Fig.  45.  With  a  sharp  knife,  cut  a  line  on  the  silvered  surface  of  a 
piece  of  looking-glass  about  5  x  10  cm.,  perpendicular  to  one  of  the 
long  edges,  and  at  its  middle  point.  With  a  thread  or  fine  rubber 
band,  fasten  the  reflector  to  the  vertical  face  of  the  block  at  B  so  that 
the  lower  end  of  the  line  on  the  looking-glass  shall  rest  upon  the 
normal  line,  DB.  Place  a  lighted  candle  at  one  end  of  a  radius, 


REFLECTION   OF   RADIANT   ENERGY.  329 

as  at  j4,  and  set  one  of  the  postal  card  screens  used  in  Experiment 
204,  near  the  edge  £>f  the  table,  and  so  that  light  from  the  candle 
will  pass  through  the  hole  and  fall  upon  the  line  marked  on  the 
mirror.  Similarly,  place  a  like  screen  on  the  other  side  of  BD, 
and  move  it  about  until,  when  looking  through  the  hole  in  it,  an 
image  of  the  hole  in  the  screen  near  A  is  seen  in  the  mirror  directly 
in  line  with  the  knife-mark  on  the  mirror.  Mark  the  points  on  the 
table  directly  under  the  perforations  in  the  screens,  and  through  them 
draw  radial  lines.  From  the  graduated  edge  of  the  table  or  with  a 
protractor,  ascertain  which  of  these  radii  makes  the  greater  angle 
with  the  radius,  BD,  perpendicular  to  the  face  of  the  mirror. 

Experiment  218.  —  Using  the  screens  and  blocks  provided  for 
Experiment  204,  arrange  apparatus  as  shown  in  Fig.  242.  At  the 
middle  of  the  middle  block,  place  a  bit  of  window  glass,  m,  painted 
on  the  under  side  with  black  varnish.  On  the  blocks  that  carry  the 
screens,  place  bits  of  glass,  n  and  o,  of  the  same  thickness  as  the  black 
mirror.  Light  from  the  candle  will  pass  through  A,  be  reflected  at 
m,  and  pass  through  B.  Place  the  eye  in  such  a  position  that  the 
spot  of  light  in 
the  mirror  may  be 
seen  through  B. 
Mark  this  spot 
with  a  needle  held 
in  place  by  a  bit 
of  wax.  Place  a 
piece  of  stiff  writ- 
ing paper  upright  FlG  L>42 
upon  m  and  n, 

mark  the  positions  of  B  and  of  m,  and  draw  on  the  paper  a  straight 
line  joining  these  two  points.  The  angle  between  this  line  and  the 
lower  edge  of  the  paper  coincides  with  the  angle  Bmn.  Reverse  the 
paper,  placing  it  upon  m  and  o.  It  will  be  found  that  the  same  angle 
coincides  with  A  mo.  The  complementary  angles,  A  mo  and  Bmn, 
being  thus  equal,  the  angle  of  incidence  equals  the  angle  of  reflection. 

272.  Law  of  the  Reflection  of  Radiant  Energy.  —  The 
angle  of  incidence  and  the  angle  of  reflection  are  equal,  and 
lie  in  the  same  plane. 


330 


SCHOOL   PHYSICS. 


273.  Explanation  of  Reflection.  —  Consider  a  beam  of 
light  as  made  up  of  a  number  of  ether  waves  moving  for- 
ward in  air  and  side  by  side,  as  represented  by  the  rays 
A,  B,  and  C.  Imagine  a  plane,  MN,  normal  to  these  rays, 
attached  to  the  waves  and  moving  forward  with  them. 
Such  a  plane  is  called  a  wave-front.  It  continues  parallel 
to  itself  and  moves  forward  in  a  straight  line.  As  the 
wave-front  advances  beyond  MN,  the  ray,  A,  strikes  the 
reflecting  surface,  RS,  and  is  turned  back  into  the  air  in 
accordance  with  the  law  just  given.  In  the  interval  of 
time  that  passes  before  the  ray,  (7,  arrives  at  P,  the  ray, 


FIG.  243. 

A,  traveling  with  unchanged  speed  as  before,  passes  over 
the  distance,  MO,  equal  to  the  distance,  NP.  This 
changes  the  direction  of  the  plane  that  is  attached  to 
the  waves,  and  sets  it  in  the  new  position  indicated  by 
OP.  Lines  drawn  from  M,  Q,  and  P,  perpendicular  to 
OP,  will  represent  the  new  direction  of  propagation,  i.e., 
the  paths  of  the  reflected  rays.  From  Fig.  243,  it  may 
easily  be  proved  that  the  angles  of  incidence  and  of  reflec- 
tion are  equal. 

274.  Apparent  Direction  of  Bodies.  —  Every  point  of  a 
visible  object  sends  a  cone  of  light  to  the  eye.  The  pupil 
of  the  eye  is  the  base  of  the  cone.  The  point  always 


REFLECTION  OF   RADIANT   ENERGY. 


331 


appears  at  the  real  or  apparent  apex  of  the  cone.  If  the 
path  of  the  light  from  the  point  in  question  to  the  eye 
is  straight,  the  apparent  position  of  the  point  is  its  real 
position.  If  the  path  is  bent  by  reflection,  or  in  any 
other  manner,  the  point  appears  to  be  in  the  direction 
of  the  light  as  it  enters  the  eye. 


Experiment  219.  —  Place  a  jar  of  water  10  or  15  cm.  back  of  a  pane 
of  glass  placed  upright  011  a  table  in  a  dark  room.  Hold  a  lighted 
candle  at  the  same  distance  in  front  of  the  glass.  The  jar  will  be 
seen  by  light  transmitted  through  the  glass.  An  image  of  the 
candle  will  be  formed  by  light  reflected  by  the  glass.  The  image  will 
be  seen  in  the  jar,  giving  the  appearance  of  a  candle  burning  in  water. 
The  same  effect  may  be  produced  in  the  evening  by  partly  raising  a 
window,  and  holding  the  jar  on  the  outside  and  the  candle  on  the 
inside.  This  experiment  suggests  an  explanation  of  many  optical 
illusions,  such  as  "  Pepper's  ghost,"  etc. 

275.  Plane  Mirrors.  — If  an  object  is  placed  before  a 
plane  mirror,  a  virtual  image  ap- 
pears behind  the  mirror.  Each 
point  of  this  image  seems  to  be 
as  far  behind  the  mirror  as  the 
corresponding  point  o'f  the  object 
is  in  front  of  the  mirror.  Hence, 
images  seen  in  still,  clear  water 
are  inverted. 

(a)  In  Fig.  244,  AB  and  AC  repre-  pIG  244. 

sent  any  two  luminous  rays  proceed- 
ing from  A  and  incident  upon  the  plane  mirror,  MR.  From  the  points 
of  incidence,  draw  the  perpendiculars,  BG  and  CF.  Draw  BE  so  that 
the  angle,  GBE,  is  equal  to  the  angle,  GBA .  Then  will  BE  represent 
the  path 'of  the  light  reflected  at  B  (§  272).  Similarly,  draw  CD  to 
represent  the  path  of  the  light  reflected  at  C.  Prolong  DC  and  EB 


332 


SCHOOL  PHYSICS. 


until  they  intersect  at  a.     Draw  A  a.     From  this  figure,  it  may  be 
proved  geometrically  that  A  IB  is  a  right  angle  and  that  A I =  al. 

276.  The   Construction   for   the  Image   produced   by  a 
plane  mirror  depends  upon  the  fact  that  the  image  of  an 

object  may  be  located  by  locat- 
ing the  images  of  a  number  of 
well  chosen  points  in  the  sur- 
face of  the  object. 

(a)  In  Fig.  245,  OB  represents  an 
arrow  in  front  of  the  mirror,  MR. 
From  the  ends  of  the  arrow,  draw  OC 
and  BD  perpendicular  to  the  face  of 
the  mirror,  and  prolong  them  indefi- 
nitely. Take  oC  equal  to  OC  and  bD 

equal  to  BD.     Join  o  and  h.     The  image  is  virtual,  erect  (i.e.,  not 

inverted),  and  of  the  same  size  as  the  object. 

Experiment  220.  —  Hinge  together  two  rectangular  pieces  of  look- 
ing-glass, each  about  7x10  cm.,  by  pasting  cloth  along  two  short 
edges,  and  set  them  on  the  table  with  an  angle  of  906  between  them. 
Set  a  "  Christmas  "  candle  or  a  bright-headed  pin  between  the  mirrors 
and  about  3  cm.  from  the  apex  of  the  angle,  and  count  the  visible 
images.  Reduce  the  angle  to  60°,  and  count  the  images.  Reduce  the 
angle  to  45°,  and  count  the  images. 

277.  Multiple  Images.  —  By  placing  two  plane  mirrors 
facing  each  other,  we  may  produce  an  indefinite  series  of 
images  of  an  object  between  them.     Each  image  acts  as  a 
material  object  with  respect  to  the  other  mirror,  in  which 
we  see  an   image    of   the   first   image,    etc.     When   the 
mirrors  are  placed  so  as  to  form  with  each  other  an  angle 
that   is   an   aliquot   part  of  360  degrees,  the  number  of 
images  is  one  less  than  the  quotient  obtained  by  dividing 
four  right  angles  by  the  included   angle,   provided  that 
quotient  is  an  even  number. 


REFLECTION  OF  RADIANT  ENERGY. 


383 


(a)  The  mirrors  will  give  three  images  when  placed  at  an  angle  of 
90° ;  five  at  60° ;  seven  at  45°. 
When  the  mirrors  are  placed 
at  right  angles,  the  object  and 
the  three  images  will  be  at 
the  corners  of  a  rectangle  as 
shown  at  A,  a,  a'  and  a". 


Experiment  221.  —  Let  a 
small  beam  of  light  fall  per- 
pendicularly upon  a  concave 
mirror.  Strike  two  black-  F!G  24(5. 

board     erasers     together    in 

front  of  the  mirror,  and  notice  that  the  light  converges  at  a  point 
not  far  from  the  mirror. 


278.  A  Focus  is  a  point  at  which  light  converges,  in 
which  case  it  is  called  a  real  focus  ;  or  it  is  a  point  from 
which  light  appears  to  proceed,  in  which  case  it  is  called 
a  virtual  focus. 

279.  Concave  Mirrors  are  generally  spherical;  i.e.,  the 
reflecting  surface  is  a  small  part  of  the  inner  surface  of  a 
spherical  shell.     The  center  of  the  sphere,  (7,  is  the  center 
of  curvature  of  the  mirror.     J.,  the  middle  point  of  the 

mirror,  is  called  the  center  or  vertex 
of  the  mirror.  Any  straight  line 
passing  through  C  to  or  from  the 
mirror  is  called  an  axis  of  the  mir- 
ror. ACX,  the  axis  that  passes 
through  J.,  is  called  the  principal 
FIG.  247.  ax*s  >  a^  other  axes  are  called 

secondary  axes.      The  angle,  MCR, 
is  called  the  aperture  of  the  mirror.     A  concave  mirror 


334 


SCHOOL  PHYSICS. 


increases  the  convergence  or  decreases  the  divergence  of 
light  that  falls  upon  it,  as  is  shown  in  Fig.  248. 


iiilffllllllllllllllllllllllil 

FIG.  248. 

Experiment  222.  —  Arrange  conjugate  parabolic  reflectors  of  pol- 
ished brass  as  shown  in  Fig.  164.  Place  a  hot  iron  ball  at  one  focus, 
and  a  bit  of  gun-cotton  that  has  been  blackened  with  lampblack  at 
the  other  focus.  Repeat  the  experiment,  holding  a  differential  ther- 
mometer so  that  one  bulb  will  be  at  the  focus,  the  second  bulb  being 
in  a  direct  line  with  the  ball  and,  therefore,  nearer  to  it.  Notice 
which  bulb  receives  the  more  heat. 

280.  The  Foci  of  Concave  Mirrors  may  be  in  front  of 
the  mirror,  in  which  case  they  are  real;  or  they  may  be 
behind  the  mirror,  in  ivhich  case  they  are  virtual. 

(a)  The  location  of  these  foci  gives  rise  to  several  cases :  — 

(1)  The  incident  rays  may  be  parallel  to  the  principal  axis,  as  they 

will  be  when  the  radiating  point  is 
at  an  infinite  distance.  Solar  rays 
are  practically  parallel.  Suppose  a 
spherical  mirror  of  small  aperture 
to  be  held  facing  the  sun.  The 
ray  that  follows  the  principal  axis 
will  fall  upon  the  mirror  perpen- 
dicularly at  A ,  and  be  reflected  back 
upon  itself.  Other  rays  will  be  re- 
flected as  shown  in  Fig.  249,  inter- 
secting at  F,  a  point  midway  between  C  and  A.  This  focus  of  rays 


JI 


>\  \ 

,-A 

^C 

c*^s 

S^J 

^    / 

'~^J 

FIG. 

/ 
249. 

/ 

REFLECTION  OF   RADIANT   ENERGY. 


335 


FIG.  250. 


parallel  to  the  principal  axis  is  called  the  principal  focus  of  the  mirror. 
The  distance,  FA,  is  called  the  principal  focal  length  or  distance  of  the 
mirror. 

(2)  When  the  rays  diverge  from  the  center  of  curvature  they  strike 
the  mirror  perpendicularly,  and  are  reflected  back  upon  themselves. 
The  radiant  point  and  the  focus  coincide. 

(3)  When  the  rays  diverge  from  a  point  beyond  the  center  of 
curvature,  as  B,  the  focus 

falls  on  the  same  axis, 
at  a  distance  from  the 
mirror  greater  than  that 
of  the  principal  focus,  and 
less  than  that  of  the  cen- 
ter of  curvature.  If  the 
radiant  point  is  at  B, 
the  focus  falls  at  6,  as 
shown  in  Fig.  250. 

(4)  When  the  rays  diverge  from  a  point  at  a  distance  from  the 
mirror  greater  than  that  of  the  principal  focus  and  less  than  that  of 
the  center  of  curvature,  we  have  the  converse  of  the  third  case.     The 
focus  falls  on  the  same  axis  beyond  the  center  of  curvature.     If  the 
radiant  point  is  at  b  (Fig.  250),  the  focus  falls  at  B.     Foci  that  are 
thus   interchangeable  are  called  conjugate  foci.     (See  §  185.)     This 
illustrates  "  the  principle  of  reversibility." 

(5)  When  the  rays  diverge  from  a  point  at  a  distance  from  the 

mirror  less  than  that  of  the 
principal  focus,  the  reflected 
rays  diverge  as  if  from  a  point 
back  of  the  mirror.  This 
point,  6,  is  a  virtual  focus. 

(6)  When  the  rays  diverge 
from  the  principal  focus,  the 
reflected  rays  are  parallel  and 
there  is  no  focus,  real  or  vir- 
tual. This  is  the  converse  of 
the  first  case. 

(6)  The  convergence  of  parallel  rays  at  the  principal  focus  is  only 
approximately  true  with  a  spherical  mirror ;  it  is.  strictly  true  with  a 
parabolic  mirror.     In  order  thaj  the  difference  between  the  spherical 
and  the  parabolic  mirror  may  be  reduced  to  a  minimum,  the  aperture 


336  SCHOOL   PHYSICS. 

of  the  former  should  be  small.  The  light  from  a  luminous  point  at 
the  focus  of  a  parabolic  mirror  is  reflected  in  truly  parallel  lines. 
The  head  lights  of  railway  locomotives  are  thus  constructed.  Para- 
bolic mirrors  would  be  more  common  if  they  were  less  expensive. 

(c)  The  sum  of  the  reciprocals  of  the  conjugate  focal  distances  is 
equal  to  the  reciprocal  of  the  principal  focal  distance.  Representing 
the  radius  of  curvature  by  r,  the  distance  of  the  luminous  point  from 
the  mirror  by/,  and  the  distance  of  the  focus  from  the  mirror  by/', 

1      1       2 


Concave  Mirror  Images. 

Experiment  223.  —  In  a  dark  room,  hold  a  candle  between  the  eye 
and  the  concave  side  of  a  bright  silver  spoon  held  a  little  ways  in 
front  of  the  face.  Notice  that  the  inverted  image  of  the  flame  is  in 
front  of  the  spoon.  Place  the  spoon  between  the  flame  and  your  face 
but  so  as  to  allow  the  face  to  be  illuminated  by  the  candle.  Notice 
the  image  of  the  observer. 

Experiment  224.  —  Place  a  concave  mirror  facing  the  sun,  and  hold 
a  bit  of  paper  so  that  its  illumination  by  the  reflected  light  is  of  the 
greatest  intensity  obtainable,  thus  locating  the  principal  focus  of  the 
mirror.  Measure  this  focal  distance.  Then  stand  directly  in  front  of 
the  mirror  and  at  a  considerable  distance  from  it.  Notice  that  the 
image  of  yourself  is  inverted,  diminished  and  real.  If  you  are  not 
sure  that  the  image  is  real,  have  some  one  hold  his  outspread  fingers 
between  the  image  and  the  mirror.  Approach  the  mirror,  and  notice 
that  your  image  increases  in  size  until  your  eye  is  at  the  center  of 
curvature.  Continue  your  approach,  and  notice  that  when  your  eye 
is  between  the  center  of  curvature  and  the  principal  focus,  no  image  is 
to  be  seen.  The  image  is  behind  you  and,  therefore,  invisible.  When 
your  eye  is  between  the  principal  focus  and  the  center  of  the  mirror, 
your  image  is  erect,  magnified  and  virtual. 

Experiment  225.  —  In  front  of  a  concave  mirror,  and  at  a  distance 
equal  to  the  radius  of  curvature,  place  a  box  that  is  open  on  the  side 
toward  the  mirror.  Within  this  box,  hang  an  inverted  bouquet  of 
bright-colored  flowers.  The  observer  should  stand  in  front  of  the 
mirror  and  some  ways  back  of  the  box.  By  giving  the  mirror  a  cer- 
tain inclination,  easily  determined  by  trial,  an  image  of  the  invisible 


REFLECTION   OF   RADIANT   ENERGY. 


337 


bouquet  will  be  seen  just  above  the  box.    A  glass  vase  may  be  placed 
upon  the  box  to  hold  the  imaged  flowers. 

Experiment  226.  —  Place  a  lighted  candle  in  front  of  a  concave 
mirror  so  that  the  flame  is  in  a  secondary  axis  of  the  mirror,  and  at  a 
distance  greater  than  the  focal  length  and  less  than  the  radius  of 
curvature.  Place  a  tracing-cloth  or  oiled-paper  screen  as  shown  in 
Fig.  252,  and,  with  a  blackened  card,  shield  it  from  the  direct  light  of 
the  candle.  Adjust  the  positions  of  the  candle  and  the  screen  until  a 


FIG.  252. 
t 

good  image  of  the  former  is  projected  on  the  latter.  If  the  outer 
edge  of  the  image  is  indistinct,  place  before  the  mirror  a  paper  cur- 
tain with  a  circular  opening  of  such  size  that  the  aperture  of  the 
exposed  part  of  the  mirror  does  not  exceed  10°.  Xotice  that  the 
image  is  less  intensely  illuminated,  but  that  its  outline  is  more  sharply 
defined. 

281.  Images  formed  by  Concave  Mirrors  consist  of  the 
conjugate  foci  of  the  several  points  in  the  surface  of  the 
object  presented  to  the  mirror  and  may,  therefore,  be  real 

or  virtual.     The  construction  of  figures  to  illustrate  the 
22 


338 


SCHOOL   PHYSICS. 


FIG.  253. 


formation  of  images  under  different  conditions  may  be 
easily  performed  by  selecting  a  few  determinative  points, 
as  the  ends  of  an  arrow,  and  determining  the  foci  of  those 
points  under  the  given  conditions. 

(a)  The  focus  of  each  point  chosen  may  be  determined  by  tracing- 
two  rays  from  the  point,  and  locating  their  real  or  apparent  inter- 
section after  reflection  by  the  mirror.  The  two  rays  most  convenient 
for  this  purpose  are  the  one  that  lies  along  the  axis  of  the  point,  and 
the  one  that  lies  parallel  to  the  principal  axis  of  the  mirror.  The 

first  of  these  is  reflected  back 
V  NJif  upon  itself,  and  the  focus 
^  r  must,  therefore,  lie  in  that 
line.  The  other  is  reflected 
through  the  principal  focus, 
and  the  construction  of  equal 
angles  of  incidence  arid  reflec- 
tion is,  therefore,  unnecessary. 
The  process  is  illustrated  in 
Fig.  253.  Following  the  order  of  the  cases  discussed  in  §  280,  it  will 
be  found  that :  — 

(1)  When  the  object  is  at  a  distance  so  great  that  the  incident  rays 
may  be  considered  parallel  (e.g.,  solar  rays),  the  image  is  formed  at 
the  principal  focus. 

(2)  When  the  object  is  at  the  center  of  curvature,  the  image  is 
real,  inverted,  of  the  same  size  as  the  object,  and  at  the  center  of 
curvature. 

(3)  When  the  object  is  at  a  distance  from  the  mirror  somewhat 
greater  than  the  center  of  curvature,  as  beyond  C,  the  image  is  real, 
inverted,  smaller  than  the  object,  and  at  a  distance  from  the  mirror 
greater   than   that   of    the    principal 

focus  and  less  than  that  of  the  center 
of  curvature,  as  between  F  and  C. 

(4)  When  the  object  is  at  a  dis- 
tance from   the   mirror  greater  than 
that  of  the  principal  focus  and  less 
than  that  of  the  center  of  curvature, 
as  between  F  and  C,  the  image  is  real, 

inverted,  larger  than  the  object,  and  FIG.  254. 


REFLECTION   OF  RADIANT   ENERGY. 


339 


at  a  distance  from  the  mirror  greater  than   that  of  the   center  of 
curvature,  as  beyond  C.     This  is  the  converse  of  the  third  case. 

(5)  When  the  object  is  at  a  distance  from  the  mirror  less  than  that 
of  the  principal  focus,  as  between  F  and  A,  the  image  is  virtual,  erect, 
and  larger  than  the  object. 

(6)  When  the  object  is  at  a  distance  from  the  mirror  equal  to  that 
of  the  principal  focus,  the  reflected  rays  are  parallel  and  no  image  is 
formed.     This  is  the  converse  of  the  first  case. 

282.   The  Spherical  Aberration  of  a  concave  mirror  is 
the  deviation  of  some  of  the  reflected  light  from  the  focus, 


FIG.  255. 


as  is  shown  in  Fig.  255.  It  arises  from  the  curvature  of 
the  mirror,  and  causes  an  indistinctness  or  blurring  of 
the  image.  Parabolic  mirrors  are  free  from  this  defect  ; 
spherical  mirrors  are  partly  freed  from  it  by  reducing 
their  apertures  so  that  the  curvature  conforms  closely  to 
the  curvature  of  a  paraboloid. 

Experiment  227.  —  Hold  the  convex  side  of  a  bright  silver  spoon 
toward  you,  and  bring  the  spoon  and  a  candle  into  the  positions  de- 
scribed in  Experiment  223.  Xotice  that  the  erect  image  of  the  flame  is 
back  of  the  spoon.  Place  the  spoon  between  the  flame  and  your  face 
but  so  as  to  allow  the  face  to  be  illuminated  by  the  candle.  Notice 
the  image  of  the  observer. 


340 


SCHOOL  PHYSICS. 


L'x 


283.    A  Convex  Mirror  is  generally  a  part  of  the  outer 
surface  of  a  spherical  shell.     It  increases  the  divergence, 

or  decreases  the  con- 
vergence of  light  that 
falls  upon  it.  The  foci 
are  virtual ;  the  prin- 
cipal focus  is  midway 
between  the  center  of 
>.<?  the  mirror  and  the  "cen- 
ter of  curvature.  The 
foci  may  be  located  and 
the  images  determined 
by  processes  closely 
similar  to  those  used 
FIG  256  for  concave  mirrors,  as 

is  sufficiently  illustrated 

by  Fig.  256.      Such  an  image  is  erect,  diminished,  and 
virtual. 

CLASSROOM  EXERCISES. 

1.  What  must  be  the  angle  of  incidence  that  the  angle  between  the 
incident  and  the  reflected  rays  shall  be  a  right  angle  ? 

2.  Copy  Fig.  245,  and  add  lines  to  show  that  the  rays  that  form  the 
image  for  the  right  eye  of  the  observer  are  different  from  the  rays  that 
form  the  image  for  the  left  eye. 

3.  With  a  radius  of  4  cm.,  describe  ten  arcs  of  small  aperture  to 
represent  the  sections  of  spherical  concave  mirrors.     Mark  the  centers 
of  curvature,  and  the  principal  foci,  and  draw  the  principal  axes.    Find 
the   conjugate   foci  for  points  in  the  principal  axis  designated   as 
follows :  (a)  At  a  distance  of  1  cm.  from  the  mirror ;   (&)  2  cm.  from 
the  mirror;   (c)  3  cm.  from  the  mirror;   (d)  4  cm.  from  the  mirror; 
(e)  6  cm.  from  the  mirror.     Make  five  similar  constructions  for  points 
not  in  the  principal  axis.     Notice  that  each  effect  is  in  consequence  of 
the  equality  between  the  angle  of  incidence  and  the  angle  of  reflection. 

4.  Illustrate  by  a  diagram  the  image  (a)  of  an  object  placed  at  the 


REFLECTION   OF   RADIANT   ENERGY. 


341 


FIG.  257. 


principal  focus  of  a  concave  mirror ;  (6)  of  one  placed  between  that 
focus  and  the  mirror ;  (c)  of  one  placed  between  the  focus  and  the 
center  of  the  mirror. 

5.  Write  a  brief  discussion  of  the  formation  of  images  by  concave 
mirrors  under  six  different 

conditions,    following    the 

order  of  the  cases  discussed 

in  §  280.      Draw  carefully 

constructed    diagrams    for        ^^        \    ^-<T^~M/ 

the  cases  not  illustrated  in 

answering  Exercise  4. 

6.  Rays  parallel  to  the 
principal  axis  fall  upon  a 
convex    mirror.       Draw    a 
diagram  to  show  the  course 
of  the  reflected  rays. 

7.  Why  do  images  formed  by  a  body  of  water  appear  inverted  ? 

8.  (a)  What  kind  of  a  mirror  always  makes  the  image  smaller  than 
the  object?     (b)  What  kind  of  a  mirror  may  make  it  larger  or  smaller, 
and  according  to  what  circumstances? 

9.  A  man  stands  before  an  upright  plane  mirror  and  notices  that 
he  cannot  see  a  complete  image  of  himself,     (a)  Could  he  see  a  com- 
plete image  by  going  nearer  the  mirror?     Why?     (b)  By  going  further 
from  it?     Why? 

10.  When  the  sun  is  30°  above  the  horizon,  its  image  is  seen  in  a 
tranquil  pool.     Wrhat  is  the  angle  of  reflection  ? 

11.  A  person  stands  before  a  common  looking-glass  with  the  left 
eye  shut.     He  covers  the  image  of  the  closed  eye  with  a  wafer  on  the 
glass.     Show  that  when,  without  changing  his  position,  he  opens  the 
left  and  closes  the  right  eye,  the  wafer  will  still  cover  the  image  of 
the  closed  eye. 

12.  The  distance  of  an  object  from  a  convex  mirror  is  equal  to  the 
radius  of  curvature.     Show  that  the  length  of  the  image  will  be  one- 
third  that  of  the  object. 

13.  From  the  formula  given  in  §  280  (c),  deduce  an  algebraic  ex- 
pression for  the  value  of  one  of  the  conjugate  focal  distances  in  terms 
of  the  principal  focal  distance  and  the  other  conjugate  focal  distance, 
and  write  its  significance  in  words. 

14.  Similarly  show  that  as  one  of  the  conjugate  focal  distances 
increases,  the  other  decreases,  and  that  when  one  of  them  becomes 


342  SCHOOL  PHYSICS. 

infinite,  the  other  coincides  in  value  with  that  of  the  principal  focal 
distance. 

15.  Considering  the  same  formula,  notice  that  if /is  less  than  half 

the  radius,  -  is  greater  than  the  principal  focal  distance,  and  that  f, 

therefore,  has  a  negative  value.     What  would  such  a  negative  value 
indicate  as  to  the  positional  character  of  the  focus  ? 

16.  Given  three  points,  A,  B  and  C,  not  in  a  straight  line.     Show, 
by  a  diagram,  how  to  place  a  plane  mirror  at  C  so  that  light  proceed- 
ing from  A  shall  be  reflected  to  B. 

17.  Show  by  a  figure  how,  with  the  aid  of  plane  mirrors,  one  can 
see  around,  or  apparently  see  through  an  opaque  object. 

18.  How  should  a  plane  mirror  be  placed  so  that  the  images  seen 
in  it  shall  have  their  natural  positions  relative  to  the  horizon  ? 

19.  Study  a  description  of  a  kaleidoscope  in  a  dictionary  or  cyclo- 
paedia, and  determine  the  number  of  mirrors  used  in  such  an  instru- 
ment that  gives  pentagrammatic  designs. 

20.  Refer  to  Fig.  255,  and  show  that  the  aberration  of  a  spherical 
mirror  may  be  lessened  by  reducing  its  aperture. 

21.  Determine  the  position  of  the  image  of  a  vertical  object  formed 
by  a  plane  mirror  placed  at  an  angle  of  45°  with  the  horizon. 

22.  The  sun's  rays  are  straight  and  practically  parallel.     How  then 
does  daylight  reach  every  nook  and  corner  of  a  room  from  which  the 
sun  is  never  visible,  e.g.,  a  room  that  has  only  a  northern  exposure  ? 

23.  Remember  that  watery  particles  in  the  air  may  reflect  light  as 
well  as  does  suspended  crayon-dust,  and  explain  the  production  of  the 
halos  often  seen  around  the  street  lamps  upon  foggy  nights. 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Bright  tin-plate,  8  x  30  cm.;  plane  and 
curved  mirrors ;  shawl-pins;  cardboard;  several  large  sheets  of  Ma- 
nila paper,  and  one  of  thin  white  paper;  a  wooden  cube,  4  or  5  cm.  on 
an  edge. 

1.  Lay  a  sheet  of  paper  on  the  table  top,  and  draw  on  it  a  straight 
line,  AB,  about  15  cm.  long,  and  mark  its  middle  point  C.  From  C, 
draw  CD  at  right  angles  to  AB,  and  10  or  15  cm.  long.  Through  D, 
draw  MN,  a  line  parallel  to  AB.  Place  the  rectangular  block  and 
mirror  used  in  Experiment  217  so  that  the  back  of  the  mirror  (the 
silvered  side)  is  exactly  over  AB,  while  the  lower  end  of  the  vertical 


REFLECTION   OF   RADIANT   ENERGY.  343 

line  that  is  marked  on  the  mirror  rests  upon  CD.  Much  of  the  suc- 
cess of  the  exercise  depends  upon  the  correct  placing  of  the  mirror. 
If  the  block  is  1  or  2  cm.  shorter  than  the  mirror,  it  will  be  easier  to 
place  the  mirror  properly.  Set  a  shawl-pin  upright  at  E,  about  3  cm. 
from  D  toward  N.  Bring  the  eye  nearly  to  the  level  of  the  paper  on 
the  other  side  of  D,  and  into  such  a  position  that  the  image  of  the  pin 
shall  be  in  line  with  the  line  scratched  on  the  mirror.  If  the  scratched 
line  and  the  image  are  not  parallel,  straighten  up  the  pin.  Set  another 
shawl-pin  upright  in  this  line  of  vision  and  in  DM,  and  mark  its  posi- 
tion F.  Draw  the  lines,  CE  and  CF.  Measure  DE  and  DF,  and  see 
how  they  compare.  If  your  work  has  been  done  accurately,  they  will 
be  equal,  but  accurate  work  must  not  be  expected.  The  mirror  may 
not  be  a  perfect  plane;  certain  lines  may  not  be  perfectly  straight, 
and  others  may  not  be  perfectly  parallel ;  the  right  angles  called  for 
may  vary  a  little  from  90° ;  and,  with  all  the  rest,  a  personal  error  is 
nearly  inevitable.  Therefore,  determine  the  ratio  that  DF  bears  to 
DE,  shift  E  to  &  new  position  a  little  further  from  D,  and  repeat  the 
work.  Then  shift  the  position  of  E  again,  and  repeat  the  work. 
The  average  of  the  three  ratios  for  DF  and  DE  will  be  pretty  close  to 
unity  if  your  work  has  been  well  done.  With  DF  and  DE  equal,  the 
work  establishes  the  equality  of  the  angles  of  incidence  and  of  reflec- 
tion. Measure  the  angles  with  a  protractor. 

2.  Continue  working  with  apparatus  and  diagram  as  in  Exercise  1. 
Move  the  pin  from  F  to  G,  2  or  3  cm.  toward  M.  In  line  with  G  and 
the  image  of  the  pin  at  E  and  near  AB,  set  a  pin,  and  mark  its  position 
G'.  Move  the  pin  from  G  to  H,  2  or  3  cm.  toward  M.  In  line  with 
H  and  the  image  of  the  pin  at  E,  and  near  AB,  set  a  pin  (that  may 
be  moved  from  G'),  and  mark  its  position  H'.  Remove  the  pins  from 
H  and  H'.  Bring  the  eye  to  the  other  side  of  D,  and  place  it  so  that 
the  pin  at  E  covers  its  image.  Set  a  pin  near  AB,  and  in  line  with  the 
pin  at  E  and  its  image.  Mark  the  position  of  this  pin  0.  Remove 
the  block,  the  mirror,  and  the  pins  at  E  and  0.  Draw  a  line  through 
the  pinholes  at  E  and  O,  and  produce  it  indefinitely  back  of  AB. 
The  part  that  lies  back  of  AB  should  be  broken  or  dotted,  and  so  in  all 
similar  cases  (see  Figs.  244  and  245).  Similarly,  produce  FC  and  the 
lines  drawn  through  the  pinholes  at  G  and  G',  and  at  H  and  H'.  The 
four  dotted  lines  should  intersect  at  a  common  point  which  mark  e. 
The  fact  that  the  image  remained  at  e  whether  the  eye  was  in  line 
with  E,  or  F,  or  G,  or  H,  shows  clearly  that  the  image  has  a  definite 
location  as  long  as  the  object  and  the  mirror  remain  stationary.  If 


344  SCHOOL  PHYSICS. 

AR  is  perpendicular  to  Ee,  as  it  should  be,  tell  what  that  fact  signi- 
fies. If  AB  bisects  Ee,  as  it  should,  tell  what  that  fact  signifies. 

3.  Draw  a  straight  line,  AB,  across  a  30  x  50  cm.  sheet  of  thin 
white  paper  midway  between  its  shorter  edges.  Set  the  block  and 
mirror  used  in  Exercise  1  with  the  foot  of  the  line  on  the  mirror  at  C, 
the  middle  point  of  AB.  Draw  on  the  paper  in  front  of  the  mirror  a 
triangle,  EFG,  no  side  of  which  is  less  than  10  cm.  long,  and  no  corner 
of  which  is  less  than  7  or  8  cm.  from  the  mirror.  Let  one  corner  of 
the  triangle  come  1  or  2  cm.  nearer  the  edge  of  the  paper  than  the  end 
of  the  mirror  does.  Paste  white  paper  over  one  face  of  a  cubical 
wooden  block  about  4  cm.  on  an  edge,  and  draw  a  vertical  ink-mark 
across  the  middle  of  the  papered  face.  This  ink-mark  is  to  replace 
the  shawl-pins  used  in  Exercises  1  and  2.  Place  this  block  with  its 
papered  face  toward  the  mirror,  and  with  the  foot  of  the- inked  line 
over  E.  Place  a  school  rule  or  other  straight-edge  on  the  paper  and, 
sighting  along  its  horizontal  edge,  bring  the  edge  into  line  with  the 
eye  and  the  image  of  the  vertical  line.  Be  sure  that  the  mirror  or  the 
wooden  cube  has  not  been  moved  from  its  proper  position,  and  try 
the  alignment  of  the  edge  of  the  rule  again.  If  it  is  correct,  hold  the 
rule  in  place  and,  with  a  well  sharpened  pencil,  tiace  a  line  on  the 
paper  along  that  edge  of  the  rule  that  is  just  under  the  edge  used  in 
taking  sight.  Mark  this  line  ElEr  Move  the  rule  into  a  new  posi- 
tion as  far  as  possible  from  the  line  just  drawn,  bring  its  edge  into 
alignment  with  the  image  of  the  vertical  line  as  before,  and  trace 
along  its  edge  a  line  which  mark  E2E2.  Then  place  the  rule  about 
midway  between  the  two  lines  drawn  on  the  paper,  bring  its  edge  into 
alignment  with  the  image  as  before,  and  trace,  as  before,  a  third  line 
which  mark  E3E3.  Be  sure  that  the  mirror  and  the  wooden  clibe  are 
still  in  their  original  positions;  if  they  have  been  moved,  test  the 
accuracy  of  the  work  already  done. 

Place  the  wooden  cube  with  the  foot  of  its  vertical  line  over  F  and, 
in  like  manner,  draw  three  lines  which  mark  F^FV  F2F2  and  F3FS. 
Similarly,  place  the  vertical  mark  over  G,  trace  three  lines  toward  its 
image,  and  mark  them  G1GV  G2G2,  and  GSG3. 

Remove  the  \vooden  cube  and  the  mirror  with  its  block,  and  pro- 
long the  lines  Ev  E*  and  Es  back  of  the  mirror  as  in  Exercise  2.  They 
should  intersect  at  a  common  point  which  mark  e,  the  location  of  the 
image  of  the  point,  E.  Similarly,  determine  the  points,  /  and  g,  the 
location  of  the  images  of  F  and  G.  Draw  the  triangle,  efg.  Fold 
the  sheet  of  paper  along  the  line  AB,  and  hold  the  folded  sheet  against 


REFLECTION   OF   RADIANT   ENERGY.  345 

the  window ;  compare  the  size  and  shape  of  the  two  triangles,  and 
their  positions  relative  to  the  line  AB.  Compare  your  results  with 
§276. 

4.  Balance  the  block  and  mirror  upon  a  rule  so  that  the  face  of 
the  mirror  crosses  the  rule  at  its  middle.     Place  the  eye  so  that  the 
further  end  of  the  rule  may  be  seen  by  looking  obliquely  downward 
and  over  the  upper  edge  of  the  mirror.     If  the  block  back  of  the 
mirror  is  visible,  move  the  mirror  up  until  it  conceals  the  top  of  the 
block,  or  use  a  thinner  block.     Adjust  the  mirror  so  that  the  further 
end  of  the  image  of  the  rule  as  seen  in  the  mirror  coincides  with  the 
end  of  the  rule  as  seen  over  the  mirror.     The  length  of  the  rule  is 
now  perpendicular  to  the  face  of  the  mirror.     Look  at  the  images  of 
the  several  divisions  of  the  scale  in  front  of  the  mirror  and  notice  the 
distance  of  each  image  back  of  the  mirror. 

5.  On  a  sheet  of  paper,  draw  two  lines,  AB  and  CD,  that  bisect 
each  other  at  right  angles  at  E.    Make  each  line  about  30  cm.  long. 
Place  the  block  and  mirror  with  its  reflecting  surface  over  AB,  and 
with  its  middle  over  E.     See  that  the  image  of  DE  visible  in  the 
mirror  is  in  line  with  the  part  of  EC  that  is  visible  back  of  the 
mirror,  as  in  Exercise  4.     This  is  a  delicate  adjustment  for  the  nor- 
mal position  of  the  mirror.     Set  the  face  of  the  mirror  so  that  it 
crosses  AB  at  E  making  acute  angles   with  AB.     Xotice  that  the 
image  of  DE  is  turned  more  than  the  mirror  is.     Set  a  shawl-pin 
upright  back  of  the  mirror,  and  in  line  with  the  image  of  DE  as  seen 
in  the  mirror.     Mark  its  position  0.     Draw  a  line  along  the  face  of  the 
mirror  through  E,  and  mark  it  MR.     Remove  the  block  and  mirror. 
Draw  the  line,  EO.     Measure  the  angles,  A  EM  and  CEO,  and  see 
how  they  compare.     Place  the  mirror  again  across  AB  at  E,  increas- 
ing the  angle,  A  EM.     Construct  the  two  angles  that   measure  the 
rotation  of  the  mirror  and  of  the  image  as  before.    Measure  and  com- 
pare them.     Once  more,  place  the  mirror  across  AB  at  E,  and  turn  it 
until  the  image  of  DE  coincides  with  EB.     Mark  on  the  paper  the 
position  of  the  face  of  the  mirror,  and  compare  the  magnitude  of  the 
angle  that  it  makes  with  A  E  with  the  magnitude  of  CEB.     State  in 
general  but  exact  terms  the  effect  that  the   deflection  of  a  plane 
mirror  has  upon  the  deflection  of  an  image  seen  in  it. 

6.  With  a  radius  of  12.5  cm.,  draw  MR,  the  arc  of  a  circle,  and 
through  its  middle  point,  C,  draw  a  tangent,  AB,  extending  about  5 
cm.   each  way  from  C.     Draw  the  radius    Cc.      Cut   a  rectangular 
piece  of  bright  tin-plate  about  8  x  30  crn.,  and  mark  a  line  across  its 


SCHOOL   PHYSICS. 

face  parallel  to  the  two  short  edges  and  midway  between  them.  Bend 
the  tin  until  its  long  edge  coincides  with  the  circular  arc  on  the  paper, 
and  hold  it  in  that  shape  by  tying  a  string  around  it.  Take  pains  to 
have  the  marked  line  on  the  concave  side,  to  avoid  "  kinking  "  the 
tin,  and  to  secure  a  uniform  curve.  Place  this  curved  reflector  over  the 
circular  arc  with  the  foot  of  its  marked  line  at  C,  and  with  the  con- 
cave side  toward  the  light.  To  test  the  accuracy  of  the  mirror,  see 
that  the  image  of  cC  is  in  a  straight  line  with  cC  itself.  Notice  the 
caustic  curves  reflected  on  the  paper,  compare  them  with  Fig.  255,  and 
remember  them  when  you  come  to  the  consideration  of  Exercise  13. 
About  4  cm.  from  C,  and  2  cm.  from  cC,  set  a  pin  upright,  as  in 
Exercise  1.  Mark  its  position  E.  Bring  the  eye  to  the  level  of  the 
paper  and  near  the  reflector,  and  set  a  second  pin  at  about  the  same 
distance  from  C,  and  in  line  with  C  and  the  image  of  the  pin  at  E. 
Mark  this  position  F.  Remove  the  curved  mirror,  and  place  the 
rectangular  block  and  plane  mirror  used  in  Exercise  1  as  therein 
directed.  The  pin  at  F,  the  line  over  C,  and  the  image  of  the  pin  at 
E  should  be  in  a  straight  line.  Remove  the  block  and  mirror.  From 
C  and  through  E  and  F,  draw  lines  of  equal  length,  CO  and  CH. 
Draw  GH  intersecting  Cc  at  D.  With  a  protractor,  measure  the 
angles,  DCG  and  DCH-,  they  should  be  about  equal.  Measure  fche 
lengths  of  DG  and  DH,  and  find  the  ratio  between  them ;  it  should  be 
nearly  unity.  Shift  E  successively  to  two  new  positions,  and  repeat 
the  work  for  each.  Find  the  average  of  the  three  ratios  between 
DG  and  DH;  it  should  be  about  unity.  If  it  is,  the  work  shows  that 
the  relation  between  the  angles  of  incidence  and  reflection  is  the 
same  for  a  concave  mirror  that  it  is  for  a  plane  mirror.  See  the 
remarks  made  under  Exercise  1. 

7.  Repeat  Exercise  6,  using  the  convex  side  of  the  mirror. 

8.  Place  a  cardboard  screen  close  behind  a  candle-flame.     Hold  a 
concave  mirror  so  that  a  sharp  image  of  the  flame  is  projected  on  the 
screen,  making  image  and  flame  coincide  as  nearly  as  possible.    Image 
and  flame  will  be  nearly  at  the  center  of  curvature  of  the  mirror. 
Describe  the  image.     Determine  the  focal  length  of  the  mirror. 

9.  Place  the  flame  between  the  center  of  curvature  of  the  mirror 
used  in  Exercise  8  and  its  principal  focus,  and  adjust  the  screen  so 
that  the  image  is  sharply  outlined  on  it.     Determine  the  distances  of 
the  flame  and  image  from  the  mirror.     Change  positions  of  the  flame 
and  screen,  holding  them  so  that  an  image  may  still  be  formed  on  the 
screen.     Does  the  principle  of  "reversibility"  hold  good  in  this  case? 


REFRACTION   OF   RADIANT   ENERGY.  347 

10.  Place  the  flame  as  near  as  possible  to  the  mirror  used  in  Exer- 
cise 8  and  still  get  an  image  on  the  screen.     What  is  the  limiting  dis- 
tance, expressed  in  general  terms? 

11.  Support  the  mirror  used  in  Exercise  8  in  a  vertical  position  at 
one  end  of  a  long  table.     Directly  in  front  and  at  the  other  end  of 
the  table  (the  distance  being  greater  than  the  radius  of  curvature), 
place  a  lighted  candle.     Place  a  small  paper  screen  so  that  a  clearly 
denned  image  of  the  flame  may  be  projected  upon  it.     Measure  the 
distances  of  the  object  and  the  image  from  the  mirror,  and  describe 
the  image.     Move  the  candle  successively  into  new  positions  nearer 
the  mirror,  projecting  and  describing  the  image,  and  making  meas- 
urements as  above  directed  for  each  position.     Compare  your  results 
with  the  statements  of  your  answer  to  Exercise  5,  page  341. 

12.  In  similar  manner,  experimentally  determine   the  effect  that 
the  position  of  the  object  has  upon   the  character  of  the  images 
formed  by  a  convex   mirror,  and  write   a  brief  discussion   of    the 
results  attained. 

13.  Put  a  pint  of  milk  into  a  shallow  circular  dish  of  bright  tin 
that  will  hold  a  quart  or  more,  and  hold  a  lamp  so  that  a  catacaustic 
curve  is  formed  on  the  surface  of  the  milk.     Account  for  the  exist- 
ence of  the  curve,  and  determine  the  relation  that  the  reflected  rays 
bear  to  the  caustic. 


IV.  REFRACTION  OF  RADIANT  ENERGY. 

f 

Experiment  228.  —  Hold  a  double-convex  lens  in  the  sun's  rays,  so 
that  the  bright  focus  on  the  side  opposite  the  sun  shall  fall  upon 
some  easily  combustible  material  like  the  tip  of  a  friction-match.  A 
spectacle-glass  will  answer,  but  a  larger  lens,  like  that  of  a  reading- 
glass,  is  desirable;  the  larger  the  lens,  the  better.  Compare  the 
effects  when  dark-colored  paper  and  white  paper  are  held  at  the 
focus.  Then  compare  the  effects  with  white  paper  that  is  clean,  and 
the  same  paper  after  it  has  been  blackened  with  a  lead  pencil,  or 
smeared  with  lampblack.  A  lens  thus  used  is  called  a  "burning- 


Experiment  229.  —  Fill  a  large  glass  globe  with  water:     An  aqua- 
rium globe  will  answer.     Hang  the  filled  globe  in  the  bright  sun- 


348 


SCHOOL   PHYSICS. 


shine  and,  at  the  focus  of  the  liquid  lens,  hold  a  bit  of  gun-cotton  that 
has  been  blackened  with  lampblack.  The  gun-cotton  may  be  thus 
ignited.  The  experiment  will  work  equally  well  if  a  large  double- 
convex  lens  of  ice  is  used  instead  of  the  globe  of  water. 

Experiment  230.  —  Place  a  coin  on  the  bottom  of  a  tin  pan  15  cm. 
or  more  in  diameter  and  4  or  5  cm.  deep,  and  lay  a  slender  straight 
rod  across  the  top  of  the  pan.  Hold  the  eye  vertically  above  the  coin, 
bring  the  rod  nearly  into  the  line  of  vision,  and  note  the  apparent 
distance  of  the  coin  below  the  rod.  Have  water  poured  into  the  pan, 
and  estimate  the  apparent  displacement  of  the  coin  if  any  is  noticed. 
Empty  the  pan  and  replace  the  coin.  Rest  the  head  against  the  edge 
of  a  shelf  or  other  convenient  fixed  support,  close  one  eye,  and  have 
the  pan  adjusted  so  that  its  side  just  hides  the  coin  from  view.  Have 
water  poured  carefully  into  the  pan  until  the  coin  is  visible.  The 
light  coming  from  the  coin  to  the  eye  is  bent  downward  somewhere 
and  somehow.  Note  the  depth  of  water  in  the  pan.  Empty  and 
wipe  the  pan,  and  repeat  the  experiment  using  kerosene  instead  of 
water,  and  compare  the  depths  of  the  two  liquids. 


Experiment  231.  —  Procure  a  clear 


FIG.  258. 


lass  bottle  with  flat  sides  not 
less  than  10  cm.  broad.  The 
larger  the  face  of  the  bottle 
the  better;  a  rectangular 
glass  battery-jar  is  still  bet- 
ter. Cover  one  face  of  the 
bottle  with  paper,  and  then 
cut  out  as  large  a  circle  as 
possible.  On  this  clear  cir- 
cular space,  mark  horizontal 
and  vertical  diameters  inter- 
secting at  i,  as  shown  in 
Fig.  258.  With  a  protrac- 
tor, graduate  the  four  quad- 
rants from  0°  at  the  ends  of 
the  vertical  diameter  to  90° 
at  the  ends  of  the  horizontal 
diameter.  Fill  the  bottle 
with  clear  water  to  the  level 
of  i,  and  hold  it  so  that  a 


REFRACTION   OF   RADIANT   ENERGY.  349 

horizontal  sunbeam  passes  through  the  clear  sides  of  the  bottle  above 
the  water.  Xotice  that  the  path  of  the  beam  through  the  bottle  is 
straight.  The  path  may  be  made  plainly  visible  by  clapping  together 
two  blackboard  erasers  so  as  to  scatter  dust  through  the  air  around 
the  bottle.  Turn  the  bottle  with  its  clear  face  to  the  front,  and  raise 
it  so  that  the  beam  passes  through  the  water.  Put  a  sheet  of  black 
paper  back  of  the  bottle,  and  notice  that  the  beam  is  still  straight. 
In  a  card,  cut  a  slit  about  5  cm.  long  and  1  mm.  wide.  Place  the  card 
against  the  bottle  as  shown  in  the  figure.  Reflect  the  beam  through 
this  slit  so  that  it  falls  upon  the  surface  of  the  water  at  i.  Xotice 
that  the  reflected  beam  is  straight  until  it  reaches  the  water,  but  that 
it  is  bent  as  it  obliquely  enters  the  water.  From  the  scale  on  the 
paper,  read  the  angles  that  the  beam  makes  with  the  vertical  diameter, 
above  and  below  /. 

Experiment  232.  —  Repeat  Experiment  231,  using  a  rectangular 
paper-weight  of  glass  instead  of  the  bottle  of  water,  and  notice 
whether  the  deviation  of  the  light  from  its  straight  path  is  more  or 
less  in  the  glass  than  it  was  in  the  water. 

284.  Refraction  of  Radiant  Energy  signifies  a  retarda- 
tion of  the  ether  waves,  and  may  be  manifested  by  a  change 
of  direction.  When  light  is  incident  on  the  surface  of  a 
transparent  medium,  part  of  it  is  reflected  as  already 
explained.  Another  part  of  the  incident  light  enters  the 
medium,  and  generally  pursues  therein  a  changed  direc- 
tion. J?his  part  is  said  to  be  refracted. 

(a)  There  is  a  change  of  direction,  i.e.,  the  radiant  energy  is 
deviated,  when  it  falls  obliquely  upon  the  interface  that  separates 
two  media,  as  air  and  water,  and  passes  from  one  to  the  other;  or 
when  it  passes  through  a  medium  the  density  of  which  is  not  uniform, 
as  the  atmosphere. 

(&)  In  Fig.  259,  LA  represents  a  ray  of  light  propagated  in 
air,  falling  obliquely  upon  the  surface  of  water  at  A,  and  deviated 
by  the  water  from  AE  to  AK.  Draw  CD  perpendicular  to  the 
refracting  surface  at  the  point  of  incidence.  LAC  is  the  angle  of 
incidence ;  KAD,  the  angle  of  refraction ;  and  KAE,  the  angle  of 


350 


SCHOOL   PHYSICS. 


deviation.     From  A  as  a  center  and  with  unity  as  a  radiu&j  describe 

a  circle,  and  draw  mn  and  pq  perpen- 
dicular to  CD.  Then  mn  is  the  sine 
of  the  angle  of  incidence;  pq  is  the 
sine  of  the  angle  of  refraction. 

(c)  For  any  two  media,  the  quo- 
tient arising  from  dividing  the  sine 
of  the  angle  of  incidence  by  the  sine 
of  the  angle  of  refraction  is  constant, 
and  is  called  the  index  of  refraction. 
The  following  table  gives  the  indices 
of  the  substances  named :  — 


Air  (0°and  760  mm.)  .  .  1.00029 

Water 1.3324 

Alcohol 1.3638 

Carbon  disulphide     .  .  .  1.6442 


Crown-glass  ....  1.515  to  1.563 

Flint-glass 1.541  to  1.710 

Diamond     2.44    to  2.755 

Lead  chromate    .  .  2.974 


The  relative  index  of  refraction  for  any  two  of  these  media  may 
be  found  by  dividing  the  index  of  one  as  given  above,  by  the  index  of 
the  other.  For  ordinary  purposes,  the  index  of  refraction  of  gases 
may  be  neglected ;  the  index  of  refraction  for  light  passing  from  air 
may  be  considered  as  1^  for  water;  lj  for  crown-glass;  If  for  flint- 
glass;  2  £  for  diamond;  and  3  for  lead  chromate.  In  this  sub-para- 
graph, refraction  has  been  discussed  as  if  light  was  homogeneous,  i.e., 
had  but  one  wave-frequency.  Subsequently,  proper  consideration  will 
be  given  to  the  fact  that  light  is  complex  in  this  respect. 

(</)  The  following  propositions  are  often  given  as  the  "  laws  of 
refraction  " : 

(1)  When  radiant  energy  passes  obliquely  from  one  medium  to  another 
of  greater  refractive  power,  it  is  bent,  at  the  point  of  incidence,  toward  a 
line  that  is  perpendicular  to  the  surface  that  separates  the  two  media. 

(2)  When  radiant  energy  passes  obliquely  from  one  medium  to  an- 
other of  less  refractive  power,  it  is  bent  from  the  perpendicular. 

(3)  The  incident  and  refracted  rays  are  in  a  plane  that  is  perpendicular 
to  the  refracting  surface. 

(4)  For  any  two  media,  the  sine  of  the  angle  of  incidence  bears  a  con- 
stant ratio  to  the  sine  of  the  angle  of  refraction. 

(e)  The  determination  of  the  direction  of  the  refracted  ray  may  be 
illustrated  as  follows:  —  Let  LA  represent  a  ray  passing  from  air  into 


REFRACTION  OF   RADIANT  ENERGY. 


351 


water  at  A.  Through  A,  draw  CD  perpendicular  to  the  refracting 
surface.  The  index  of  refrac- 
tion for  the  two  media  is  f. 
From  A  as  a  center  and  with 
radii  that  are  to  each  other  as 
4:3,  draw  concentric  circles. 
Prolong  LA  to  E.  From  y,  the 
intersection  of  AE  with  the 
circumference  of  the  inner  cir- 
cle, draw  vp  parallel  to  CD. 
Through  />,  the  intersection  of 
this  line  with  the  circumfer- 
ence of  the  outer  circle,  draw 
A  K,  the  line  sought.  Drawing 
pq,  vw,  and  mn  perpendicular  to 
CD,  it  may  be  shown  geomet- 
rically that 

sin  LAC      mn     4 

— — TT-TT;  —         :  o'    the  index  of  refraction  for  air  and  water. 

sin  KAD     pq      3 

(/)  If  the  ray  passes  in  the  opposite  direction,  i.e.,  from  water  into 
air,  the  process  is  the  reverse  of  that  just  indicated.  Let  KA  repre- 
sent the  incident  ray.  Through  p,  draw  pv.  Through  u,  draw  EA 
and  prolong  it  to  L.  AL  is  the  direction  sought.  In  some  cases 
it  will  be  more  convenient  to  use  the  equivalent  process  of  continuing 
KA  to  0,  drawing  oi  parallel  to  CD,  and  drawing  the  refracted  ray 
from  A  through  {. 

((7)  According  to  the  forms  and  relative  positions  of  their  refract- 
ing surfaces,  there  are  thDee  kinds  of  refractors ;  plates,  prisms  and 
lenses. 

Total  Reflection. 

Experiment  233.  —  Place  the  bottle  used  in  Experiment  231,  upon 
a  block  on  the  table.  Invert  the  card  so  that  its  horizontal  slit  is 
near  the  bottom  of  the  bottle.  Place  a  mirror  on  the  table  and  close 
to  the  card.  With  a  hand-mirror,  reflect  a  sun-beam  downward  upon 
the  mirror  on  the  table  so  that  it  will  be  reflected  obliquely  upward, 
passing  through  the  slit  in  the  card  and  through  the  water  toward  i. 
Diffuse  crayon-dust  through  the  air  near  the  bottle,  and  notice  the 
refraction  of  the  beam  as  it  leaves  the  water.  Bring  the  slit  gradually 
higher,  changing  the  position  of  the  hand  mirror  so  that,  as  the  rays 


352 


SCHOOL  PHYSICS. 


pass  through  the  slit  and  upward  through  the  water  to  i,  the  angle  of 
incidence  is  gradually  increased.  Notice  that  the  angle  of  refraction 
increases  more  rapidly  than  the  angle  of  incidence.  As  the  angle 
of  incidence  changes  from  47°  or  48°  to  49°  or  50°,  closely  observe 
the  refracted  light  which  approaches  the  refracting  surface  more  and 
more  closely.  When  the  angle  of  incidence  has  a  certain  magnitude, 
the  refracted  ray  coincides  with  the  surface  of  the  water ;  i.e.,  the 
angle  of  refraction  has  reached  its  maximum  value,  90°.  If  the  angle 
of  incidence  is  still  further  increased,  the  light  cannot  emerge  at  i, 
but  will  be  reflected  downward  as  if  the  plane  between  the  water  and 
the  air  was  a  perfect  mirror. 

Experiment  234.  —  Place  a  bright  spoon  in  a  tumbler  of  water  with 
the  handle  leaning  from  you.  Hold  the  tum- 
bler considerably  above  the  level  of  the  eye. 
Notice  that  you  see  not  only  the  lower  part  of 
the  spoon  in  the  water  but  also  an  image  of  the 
shank  of  the  spoon  above  the  upper  surface  of 
the  water.  The  free  liquid  surface  glistens  and 
reflects  as  does  a  mirror. 

285.  Total  Reflection.  —  When  a  ray 
of  light  passes  obliquely  from  a  medium 
of  higher  to  one  of  lower  refractive 
power,  the  angle  of  refraction  is  always 
greater  than  the  angle  of  incidence. 
FIG.  201.  The  angle  of  incidence  may  be  in- 

creased until  the  angle  of 
refraction  is  90°,  as  repre- 
sented by  the  ray,  DFM. 
A  further  increase  in  the 
angle  of  incidence  cannot 
result  in  an  increase  of  the 
angle  of  refraction.  Con- 
sequently, the  ray  cannot 
obey  the  laws  of  refraction, 


i^=^^s-<—^_  ^£ j N 


FIG.  262. 


REFRACTION  OF  RADIANT  ENERGY. 


353 


but  does  obey  the  laws  of  reflection  as  represented  by  the 
ray,  DGrO.  It  is  totally  reflected  at  the  point  of  incidence 
back  into  the  former  medium.  The  angle  of  incidence  at 
which  the  effect  changes  from  refraction  to  internal  re- 
flection is  called  the  critical  angle. 

(a)  The  magnitude  of  the  critical  angle  varies  with  the  media 
employed.  For  (air  and)  water,  it  is  about  48^°;  for  crown-glass, 
about  41° ;  for  diamond,  about  24°.  The  reflection  is  called  "  total " 
because  all  of  the  incident  light  is  reflected,  which  is  never  the  case 
in  ordinary  reflection. 

(&)  To  construct  the  critical  angle,  draw  concentric  circles  as  in 
Fig.  260,  the  ratio  of  their  radii  being  the  index  of  refraction  for  the 
media  used.  Remember  that  the  emergent  ray  must  graze  the  surface 
of  the  water,  and  reverse  the  process  described  in  §  284  (/).  At  the 
point  where  AN  intersects  the  inner  circle,  erect  a  perpendicular. 
The  point  where  this  normal  intersects  the  outer  circle  will  lie  in  the 
prolongation  of  the  ray  incident  at  A. 

286.  Cause  of  Refraction.  —  It  is  easy  to  conceive  of  the 
motions  of  the  ether  as  being  hindered  by  the  particles  of 
the  matter  that  is 
permeated  by  the 
ether.  Thus,  when 
ether  waves  that 
constitute  light 
are  transmitted 
through  glass,  they, 
are  hindered  by 
the  molecules  of 
the  glass,  and  im- 
part some  of  their 
motion  to  those 
molecules  ;  i.e.,  a 


FIG.  263. 


part  of  the  light  is  absorbed. 
23 


When  a  beam  of  light,  as 


354  SCHOOL  PHYSICS. 

» 

represented  by  the  rays  A,  B,  and  (7,  moves  forward  in 
the  air,  the  wave-front,  J£ZV(see  §  273),  continues  parallel 
to  itself  and  moves  forward  in  a  straight  line.  As  the 
wave-front  advances  beyond  MN,  the  ray,  A,  enters  the 
glass,  while  B  and  0  are  still  in  the  air.  The  advance  of 
A  in  the  glass  is  retarded  by  the  glass  so  that,  while  C  is 
passing  in  air  from  NtoP,  A  traverses  the  shorter  path, 
MO.  This  retardation  of  A  and  the  corresponding  re- 
tardation of  B  change  the  direction  of  the  plane  that  is 
attached  to  the  waves,  and  set  it  in  the  new  position 
indicated  by  OP.  All  of  the  rays  having  entered  the 
glass,  the  wave-front  again  moves  forward  in  a  straight 
course,  normal  to  OP,  representing  the  new  direction  of 
propagation.  In  passing  into  the  glass  the  direction  of  the 
beam  was  changed,  a  direct  result  of  a  change  of  speed  at 
the  surface  of  the  glass.  This  phenomenon  is  called  refrac- 
tion. The  beam  was  bent  toward  a  perpendicular  to  the 
bounding  surface,  RS.  When  the  beam  emerges  from 
the  glass,  similar  changes  will  take  place  in  inverse  order, 
and  the  beam  will  be  bent  from  the  perpendicular  to  the 
refracting  surface. 

(«)  The  index  of  refraction  is  numerically  equal  to  the  ratio 
between  the  velocity  of  the  incident  light  and  the  velocity  of  the 
refracted  light. 

Refraction  by  Plates. 

Experiment  235.  —  Draw  a  straight  line  of  such  length  that  it  ex- 
tends both  ways  beyond  the  ends  of  a  piece  of  thick  plate-glass 
placed  upon  it.  Look  obliquely  through  the  glass  and  from  the 
side  of  the  line,  and  notice  the  apparent  displacement  of  the  part 
of  the  line  seen  through  the  plate. 

287.  Refraction  by  Plates.  — When  radiant  energy  passes 
through  a  medium  bounded  by  parallel  planes,  the  refrac- 


REFRACTION  OF  RADIANT  ENERGY. 


355 


tions  at  the  two  surfaces  are  equal  and  contrary  in 
direction.  The  direction  after 
passing  through  the  plate  is 
parallel  to  the  direction  be- 
fore entering  the  plate  ;  the  rays 
merely  suffer  lateral  aberration. 
Objects  seen  obliquely  through 
such  plates  appear  slightly  dis- 
placed from  their  true  position. 


FIG.  264. 


288.  A  Prism  is  a  transparent  body  with  two  refracting 
surfaces  that  lie  in  intersecting  planes.  The  angle  formed 
by  these  planes  is  called  the  refracting  angle. 

(a)  Let  mno  represent  the  principal  section  of  a  prism.     A  ray  of 

light  from  L  is  refracted 

<£^  at  a  and   b,   and    enters 

I  j     \^-  the  eye  in  the  direction 

'\  bE.     The    object,    being 

seen  in  the  direction  of 
the  ray  as  it  enters  the 
eye,  appears  to  be  at  I. 
An  object  seen  through 
a  prism  seems  to  be 
moved  in  the  direction  of 
the  refracting  angle ;  the 
FIG.  265.  rays  are  bent  away  from 

the  refracting  angle. 

(&)  Cathetal  prisms  readily  yield  the  phenomena  of  total  reflection 
as  shown  in  Fig.  266,  and  are  often  used  when  light 
is  to  be  turned  through  a  right  angle. 


v 


Experiment  236.  —  Make  a  monochromatic  light  by 
sprinkling  a  little  table-salt  on  the  wick  of  an  alco- 
hol lamp.  Place  the  flame  on  the  level  of  the  per- 
foration in  one  of  the  postal  card  screens  used  in 
Experiment  204.  Back  of  this  screen,  place  another  so  that  the 


FIG.  266. 


356  SCHOOL  PHYSICS. 

light  from  the  lamp  passing  through  the  perforation  of  the  first 
makes  a  spot  on  the  second.  Mark  the  position  of  the  spot.  Behind 
the  first  screen  and  close  to  it,  hold  a  glass  prism  with  its  refracting 
edge  uppermost,  horizontal,  and  parallel  to  the  screen.  Adjust  its 
height  so  that  the  rays  passing  through  the  perforation  also  pass 
through  the  prism.  Notice  that  the  spot  of  light  on  the  second 
screen  is  moved  downward.  Mark  the  new  position  of  the  spot. 

289.  The  Angle  of  Deviation  of  rays  thus  refracted  is 
the  difference  in  direction  between  the  incident  and  emer- 
gent rays.    In  Experiment  236,  this  angle  may  be  roughly 
described  as   the   angle   between  lines  drawn  from    the 
perforation  in  the  first  screen  to  the  two  marked  positions 
of  the  luminous  spot  on  the  second  screen.     In  Fig.  265, 
imagine  La  extended  until  it  intersects  El  at  x.     The 
angle  Lxl  is  the  angle  of  deviation.      The  angle  varies 
with  the  magnitude  of  the  refracting  angle  of  the  prism, 
its  index  of  refraction,  the  wave-length  of  the  light  used, 
and  the  angle  of  incidence.     Other  conditions  being  simi- 
lar, a  prism  gives  the  least  deviation  when  the  angles  of 
incidence  and  of  emergence  are  equal. 

(a)  The  position  of  a  prism  for  minimum  deviation  is  easily  deter- 
mined by  looking  through  it  at  an  object,  as  in  Fig.  265,  and  turning 
the  prism  until  the  changing  apparent  position,  I,  comes  to  a  stand- 
still, and  begins  to  move  backward. 

290.  A  Lens  is  a  transparent  body  the  two  refracting 
surfaces  of  which  are  curved,  or  one  of  which  is  curved 
and  the  other  plane.     Lenses  are  generally  made  of  crown- 
glass  which  is  free  from  lead,  or  of  flint-glass  which  con- 
tains lead  and  has  greater  refractive  power.     The  curved 
surfaces  are  generally  spherical. 

(a)  With  respect  to  their  surfaces,  lenses  are  of  two  classes,  with 
three  varieties  of  each :  — 


REFRACTION  OF   RADIANT  ENERGY. 
(1.)  Double-convex, 


(2.)  Plano-convex, 

(3.)  Meniscus,  converging. 


357 

I  Thicker  at  the  middle  than  at  the  edges ; 


FIG.  267. 

The  double-convex  (biconvex  or  magnifying)  lens  may  be  taken  as 
the  type  of  these ;  its  effects  may  be  considered  as  produced  by  two 
prisms  with  their  bases  in  contact. 

(4.)  Double-concave,    ] 

(5.)  Plano-concave,      [ Thinner  at  the  middle  than  at  the  edges ; 

(6!)  Concavo-convex,  J      diver^ng' 

The  double-concave  (biconcave)  lens  may  be  taken  as  the  type  of 
these  ;  its  effects  may  be  considered  as  produced  by  two  prisms  with 
their  refracting  edges  in  contact. 

(6)  A  double-convex  lens  may  be  described  as  the  part  common  to 
two  spheres  that  intersect  each  other.  The  centers  of  the  limiting 
spherical  surfaces, 

as   c    and    C,    are  ...-•"    "•-,       -'"" 

the  centers  of  curva- 
ture. The  straight 
line,  XY,  passing 
through  the  cen- 
ters of  curvature 
is  the  principal  axis 
of  the  lens.  In  the 
piano-lenses,  the 
principal  axis  is  a 
line  drawn  from  the  center  of  curvature  normal  to  the  plane  surface. 
A  point  on  the  principal  axis  so  taken  that  rays  passing  through  it 
pierce  parallel  elements  of  the  refracting  surfaces  is  called  the  optical 
center.  A  ray  passing  through  the  optical  center  suffers  no  change  of 
direction  other  than  a  slight  lateral  aberration  that  may  be  disre- 
garded. When  the  two  spherical  surfaces  are  of  equal  curvature,  thy 


358  SCHOOL  PHYSICS. 

optical  center  is  at  equal  distances  from  the  two  faces  of  the  lens,  i.e., 
at  its  center  of  volume.  For  the  piano-lenses,  the  optical  center  lies 
on  the  curved  surface ;  for  the  meniscus,  it  lies  outside  the  lens  and 
on  the  convex  side ;  for  the  concavo-convex  lens,  it  lies  outside  the 
lens  and  on  the  concave  side.  Any  straight  line,  other  than  the 
principal  axis,  passing  through  the  optical  center  is  a  secondary  axis. 

(c)  To  trace  a  ray  through  a  lens,  we  have  only  to  apply  the  prin- 
ciples already  explained.  For  example,  let  LN  represent  a  glass  bi- 
convex lens  (index  of  refraction,  f)  with  centers  of  curvature  at  C  and 


C",  and  AB,  the  incident  ray.  From  B  as  a  center,  draw  the  arcs,  mn 
and  op,  making  the  ratio  of  iheir  radii  equal  to  the  index  of  refraction, 
i.e.,  2 : 3.  Draw  the  normal,  C'B.  Draw  st  parallel  to  C'B.  Draw 
the  straight  line  tBDy ;  BD  is  the  path  of  the  ray  through  the  lens. 
From  D  as  a  center,  draw  the  arcs,  uv  and  wx,  using  the  same  radii  as 
for  mn  and  op.  Draw  the  normal,  CD.  Draw  yz  parallel  to  CD. 
Draw  DzA',  the  path  of  the  ray  after  emergence. 

Experiment  237.  —  Hold  one  of  the  large  lenses  of  an  opera  glass 
or  optical  lantern  in  the  sun's  rays.  Notice  the  converging  pencil 
formed  by  the  light  (after  passing  through  the  lens)  as  it  passes 
through  air  made  dusty  by  striking  together  two  blackboard  erasers. 
The  focus  and  its  distance  from  the  lens  may  be  seen.  Measure  this 
distance.  Hold  a  similar  lens  by  the  other,  face  to  face.  Notice  that 
the  light  after  passing  through  both  lenses  converges  more  quickly, 
lessening  the  distance  of  the  focus  from  the  lens. 

291.  The  Foci  of  Convex  Lenses  may  be  determined 
experimentally,  but  some  of  their  properties  are  more  con- 


KEFKACTION   OF   RADIANT  ENERGY.  359 

veniently  studied  by  the  diagrammatical  tracing  of  rays  in 
accordance  with  the  principles  and  processes  already 
studied.  To  locate  the  focus  for  light  diverging  from 
any  point,  it  is  necessary  to  determine  the  point  of  inter- 
section of  two  emergent  rays.  The  problem  is  much 
simplified  by  considering  the  axis  that  passes  through  the 
point  of  divergence  as  the  path  of  one  of  these  rays. 

(a)  For  converging  lenses,  the  reciprocal  of  the  principal  focal  dis- 
tance equals  the  sum  of  the  reciprocals  of  any  pair  of  conjugate  focal 
distances. 

1_1      !_ 

f~P+Pr 

(6)  Experimental  work  with  convex  lenses,  and  a  careful  study  of 
this  formula,  develop  frequent  analogies  to  the  phenomena  of  concave 
mirrors,  and  give  rise  to  several  cases  as  follows  :  — 

(1)  When  the  incident  rays  are  parallel  to  the  principal  axis,  their 
focus  is  called  the  principal  focus.     With  a  biconvex  lens  of  crown- 
glass  (index  of  refraction,  f)  the  principal  focus  is.  at  the  center  of 
curvature,  i.e.,  the  focal  length  of  the  lens  is  equal  to  the  radius  of 
curvature.     With  a  plano-convex  lens,  the  focal  length  is  twice  the 
radius  of  curvature.     In  either  case,  the  focus  is  real. 

(2)  When  the  incident  rays  diverge  from  a  point  more  than  twice 
the  focal  distance  from  the  lens,  a  real  focus  is  formed  on  the  other 
side  of  the  lens,  and  at  a  distance  greater  than  the  focal  length  and 
less  than  twice  the  focal  length.     (See  A  and  A',  Fig.  269.) 

(3)  When  the  incident  rays  diverge  from  a  point  at  twice  the  focal 
distance  from  the  lens,  a  real  focus  is  formed  on  the  other  side  of  the 
lens  and  at  the  same  distance  from  it.     These  two  points,  as  c  and  c' 
in  Fig.  269,  are  called  secondary  foci. 

(4)  When  the  incident  rays  diverge  from  a  point  distant  from  the 
lens  more  than  the  focal  length  and  less  than  twice  the  focal  length, 
a  real  focus  is  formed  on  the  other  side  of  the  lens  and  at  a  distance 
greater  than  twice  the  focal  length.      This  is  the   converse  of  the 
second  case.     Two  foci  that  are  thus  interchangeable,  like  A  and  A' 
in  Fig.  269,  are  called  conjugate  foci.     The  secondary  foci  are  con- 
jugate. 

(5)  When  the  incident  rays  diverge  from  the  principal  focus,  the 


360  SCHOOL  PHYSICS. 

emergent  rays  will  be  parallel,  and  no  focus,  real  or  virtual,  will  be 
formed.     This  is  the  converse  of  the  first  case. 

(6)  When  the  incident  rays  diverge  from  a  point  nearer  the  lens 
than  the  principal  focus,  the  emergent  rays  are  still  diverging,  and  a 
virtual  focus  is  formed  back  of  the  radiant  point. 

(7)  When  the  incident  rays  are  converging,  a  real  focus  is  formed 
on  the  other  side  of  the  lens  at  a  distance  less  than  the  focal  length. 
This  is  the  converse  of  the  sixth  case. 

(ft)  Each  pupil  should  draw  a  figure  to  illustrate  each  of  the  fore- 
going cases. 

292.  The  Foci  of  Concave  Lenses  may  be  located  by 
processes  already  studied.  Such  lenses  have  their  centers 
of  curvature,  their  primary  and  secondary  axes,  and  their 
optical  centers  the  same  as  convex  lenses. 

(a)  For  diverging  lenses,  the  reciprocal  of  the  principal  focal  dis- 
tance equals  the  difference  of  the  reciprocals  of  any  pair  of  conjugate 
focal  distances. 

1=1-1 

/  P  / 

(&)  Experimental  work  with  concave  lenses,  and  a  careful  study  of 
this  formula,  develop  frequent  analogies  to  the  phenomena  of  convex 
mirrors,  and  give  rise  to  several  cases  as  follows  :  — 

(1)  When  the  incident  rays  are  parallel  to  the  principal  axis,  the 
emergent  rays  diverge  as  if  they  came  from  a  virtual  focus,  which  is 
called  the  principal  focus.     With  a  biconcave  lens  of  glass  (index  of 
refraction,  f),  the  principal  focus  is  at  the  center  of  curvature.     With 
a  plano-concave  lens,  the  focal  length  is  twice  the  radius  of  curvature. 

(2)  When  the  incident  rays  are  diverging,  the  focus  is  virtual  and 
at  a  distance  from  the  lens  less  than  the  focal  length.     As  the  radiant 
point  approaches  the  lens,  the  focus  also  approaches  the  lens. 

(3)  When  the  incident  rays  are  converging,  the  effects  are  varied 
according  to  the  degree  of  convergence.     If  the  point  of  convergence 
is  nearer  the  lens  than  the  principal  focus,  a  real  focus  will  be  formed 
at  a  distance  greater  than  the  focal  length  of  the  lens.     If  the  point 
of  convergence  is  at  the  principal  focus,  the  emergent  rays  will  be 
parallel,  and  no  focus  will  be  formed.     If  the  point  of  convergence  is 
further  from  the  lens  than  the  principal  focus,  a  virtual  focus  will  be 
formed. 


REFRACTION  OF  RADIANT  ENERGY. 


361 


(&)  Each  pupil  should  draw  a  figure  to  illustrate  each  of  the  fore- 
going cases. 

Images. 

Experiment  238.  —  Repeat  Experiment  228,  and  measure  the  focal 
length  of 'the  lens. 

Experiment  239.  —  Place  a  candle,  a  convex  lens,  and  a  screen  in 
line  as  shown  in  Fig.  270,  the  distance  of  the  candle  from  the  lens 


FIG.  270. 

being  a  little  greater  than  the  focal  length  of  the  lens.  Adjust  the 
position  of  the  screen  until  a  sharply  defined  image  of  the  candle  is 
projected  upon  it.  Place  the  eye  back  of  the  screen  and  have  the 
screen  removed ;  the  inverted  image  may  be  seen  suspended  in 
mid-air.  Burn  touch-paper  under  the  image,  and  notice  its  projec- 
tion on  the  screen  of  smofce.  Replace  the  screen  first  used. 

Experiment  240.  —  With  candle  and  screen  in  positions  as  described 
in  Experiment  239,  adjust  the  position  of  the  lens  so  that  the  flame 
and  the  image  of  the  flame  are  of  the  same  size.  Measure  the  dis- 
tance of  the  screen  from  the  candle,  and  compare  a  quarter  of  that 
distance  with  the  focal  length  of  the  lens. 

293.  Images  Formed  by  Lenses  consist  of  the  conjugate 
foci  of  the  several  points  in  the  surface  of  the  object  pre- 
sented to  the  lens  and  may,  therefore,  be  real  or  virtual. 
The  construction  for  such  images  is  closely  analogous  to 
the  process  employed  with  mirrors. 


362 


SCHOOL  PHYSICS. 


(a)  The  focus  of  each  point  chosen  may  be  determined  by  tracing 
two  rays  from  the  point,  and  locating  their  real  or  apparent  intersec- 
tion after  emerging  from  the  lens.  The  two  rays  most  convenient 
for  this  purpose  are  the  one  that  lies  along  the  secondary  axis  of  the 
point,  and  the  one  that  lies  parallel  to  the  principal  axis  of  the  lens. 
For  example,  from  A  and  E,  extremities  of  an  arrow,  draw  the 
secondary  axes,  AOa  and  EOe.  From  A,  draw  AB  parallel  to  the 


E 


FIG.  271. 

principal  axis,  XY.  Determine  the  direction  of  BD  by  construction. 
From  D,  draw  the  path  of  the  emergent  ray  through  the  principal 
focus,  F.  It  intersects  the  secondary  axis  at  a,  the  conjugate  focus 
of  the  radiant  point,  A.  In  similar  manner,  the  conjugate  focus  of 
the  point,  E,  may  be  located  at  e.  The  points,  a  and  e,  mark  the  ex- 
tremities of  the  image  of  the  object,  A  E. 

(b)  An  examination  of  Fig.  271  shows  that  the  linear  dimensions 
of  object  and  image  are  directly  as  their  respective  distances  from  the 
center  of  the  lens ;  they  will  be  virtual  or  real,  erect  or  inverted,  ac- 
cording as  they  are  on  the  same  side  of  the  lens,  or  on  opposite  sides. 

Experiment  241.  —  Select  a  large  biconvex  lens,  and  cut  a  card- 
board disk  of  the  same  diameter.  Punch  a  ring  of  small  holes  near 
the  circumference  of  the  disk,  and  cut  a  hole  about  2  cm.  in  diam- 
eter at  its  center.  Cut  a  notch  in  the  border  of  one  of  the  small 
holes  as  a  distinguishing  mark.  Place  the  lens  in  the  path  of  a 
beam  from  the  porte  lumiere,  and  cover  one  of  its  faces  with  the 
perforated  disk.  Hold  a  screen  near  the  lens  and  so  that  the  refracted 
rays  fall  upon  it.  Slowly  move  the  screen  away  from  the  lens  until 
you  find  the  focus  of  the  light  that  passes  through  the  small  holes. 
Moving  the  screen  still  further,  you  will  find  another  focus  for  the 
light  that  passes  through  the  central  opening  in  the  disk.  Notice 


REFRACTION  OF   RADIANT   ENERGY.  363 

that  the  rays  that  pass  through  the  marginal  holes  cross  before 
reaching  the  screen,  and  form  a  ring  of  luminous  spots  around  the 
central  image. 

294.  Spherical  Aberration.  — The  rays  that  pass  through 
a  spherical  lens  near  its  edge  are  deviated  more  than 
those  that  pass  nearer  the  center.  They,  therefore,  con- 
verge nearer  the  lens.  This  unequal  deviation  is  called 
spherical  aberration.  The  indefiniteness  of  focus  causes  a 
blurring  of  the  image.  In  practice,  the  marginal  rays  are 
often  cut  off  by  an  annular  screen  called  a  diaphragm,  or 
the  curvature  of  the  lens  is  lessened  toward  its  edge. 
A  lens  thus  corrected  for  spherical  aberration  is  called 
aplanatic. 

CLASSROOM  EXERCISES. 

1.  Remembering  the  varying  density  of  the  earth's  atmosphere, 
draw  a  diagram  showing  that  the  sun  may  be  seen  before  it  has  as- 
tronomically risen,  and  after  the  true  sunset,  i.e.,  after  it  has  dipped 
below  the  western  horizon. 

2.  (a)  Name,  and  illustrate  by  diagram,  the  different  classes  of 
lenses.     (6)  Explain,  with  diagram,  the  action  of  the  burning-glass. 

3.  Draw  circles  so  that  parts  of  their  circumferences  may  represent 
the  curved  surface  of  a^  meniscus,  a  biconcave,  and  a  concavo-convex 
lens. 

4.  (a)  Describe  the  phenomena  of  total  reflection.     (7>)  Show,  with 
diagram,  how  the  secondary  axes  of  a  lens  mark  the  limits  of  the 
image. 

5.  Construct  the  critical  angle  for  air  and  water. 

6.  Show  how  a  beam  of  light  may  be  bent  at  a  right  angle  by  a 
glass  prism. 

7.  Trace  a  ray  through  a  biconcave  lens,  using  the  process  em- 
ployed in  §  290  (c)  for  the  biconvex  lens. 

8.  Trace  a  ray  through  a  biconvex  lens  for  the  location  of  its 
principal  focus. 

9.  Trace  a  ray  through  a  biconcave  lens  for  the  location  of  its 
principal  focus. 


364  SCHOOL  PHYSICS. 

10.  Through  what  point  does  the  line  joining  the  conjugate  foci  of 
a  convex  lens  always  pass  ? 

11.  Construct  the  images  formed  by  a  convex  lens  under  the  six 
following  cases  and  describe  each  image :  (a)  when  the  incident  rays 
are   practically  parallel;  (6)  when   the   object   is  a  little  beyond  a 
secondary  focus ;  (c)  when  the  object  js  at  a  secondary  focus ;  (e?) 
when  the  object  is  between  secondary  and  principal  foci ;  (e)  when 
the  object  is  at  the  principal  focus ;  (/)  when  the  object  is  between 
the  principal  focus  and  the  lens. 

12.  (a)  The  focal  distance  of  a  convex  lens  being  6  inches,  deter- 
mine the  position  of  the  conjugate  focus  of  a  point  12  inches  from 
the  lens,     (b)  18  inches  from  the  lens. 

13.  The  focal  distance  of  a  convex  lens  is  30  cm.     Find  the  con- 
jugate focus  for  a  point  15  cm.  from  the  lens. 

14.  If  an  object  is  placed  at  twice  the  focal  distance  of  a  convex 
lens,  how  will  the  length  of  the  image  compare  with  the  length  of  the 
object  ? 

15.  A  small  object  is  12  inches  from  the  lens;  the  image  is  24 
inches  from  the  lens  and  on  the  opposite  side.     Determine  (by  con- 
struction) the  fdcal  distance  of  the  lens. 

16.  A  candle-flame  is  6  feet  from  a  wall ;  a  lens  is  between  the 
flame  and  the  wall,  5  feet  from  the  latter.     A  distinct  image  of  the 
flame  is  formed  upon  the  wall,     (a)  In  what  other  position  may 
the  lens  be  placed,  that  a  distinct  image  may  be  formed  upon  the 
wall  ?     (6)  How  will  the  lengths  of  the  images  compare  V 

17.  Why  does  a  sphere  under  water  look  like  a  spheroid  V 

18.  When  clear  glass  is  pounded  into  small  particles,  it  becomes 
opaque.     Explain. 

LABORATORY  EXERCISES. 

Additional    Apparatus,   etc.  —  Lenses ;    spy-glass ;    wooden    cubes 
grooved  and  fitted  as  described  in  Exercise  12. 

1.  Trace  a  ray  passing  obliquely  from  air  into  glass  (index  of 
refraction,  1.5). 

2.  Trace  a  ray  passing  obliquely  from  glass  into  air. 

3.  Trace  a  ray  passing  obliquely  from  air  into  water  (index  of 
refraction,  1.3). 

4.  Trace  a  ray  passing  obliquely  from  water  into  air. 

5.  Trace  a  ray  passing  obliquely  from  air  into  diamond  (index  of 
refraction,  2.5). 


REFRACTION  OF  RADIANT  ENERGY.  365 

6.  Trace  a  ray  passing  obliquely  from  water  into  glass. 

7.  Trace  a  ray  passing  through  water  toward  air  so  that  the  angle 
of  incidence  is  50°.     (See  §  285,  a.) 

8.  Hold  a  test-tube  partly  immersed  in  water  so  that  its  length  is 
slightly  inclined  from  a  vertical.     Look  down  through  the  water  upon 
the  immersed  part  of  the  air-filled  tube,  and  notice  that  it  looks  like 
highly  polished  silver.      Fill  the  test-tube  with  water,  and  write  an 
explanation  of  the  change  in  its  appearance. 

9.  Make  a  concave  air-lens  and  place  it  in  water.     Make  a  con- 
vex water-lens  and  place  it  in  air.     Compare  the  effects  of  the  two 
lenses  upon  beams  of  light  that  pass  through  them. 

10.  Adjust  a  candle-flame  and  a  screen  on  opposite  sides  of  a  bi- 
convex lens  so  that  a  sharp  image  of  the  flame  is  projected  on  the 
screen  when  flame  and  screen  are  at  equal  distances  from  the  lens. 
Record  the  focal  length  of  the  lens,  the  names  of  the  positions  occu- 
pied by  flame  and  screen,  and  a  description  of  the  image.     Exchange 
the  positions  of  the  flame  and  the  screen,  and  test  the  principle  of 
"  reversibility."     Slowly  diminish  the  distance  between  lens  and  can- 
dle until  it  is  impossible  to  place  the  screen  so  as  to  obtain  an  image. 
Measure  this  distance,  compare  it  with  the  focal  distance  of  the  lens, 
and  indicate  the  significance  of  the  comparison.     With  the  lens  at 
four  different  distances  from  the  screen,  form  images.     In  each  case, 
measure  the  linear  dimensions  of  flame  and  image,  and  the  distances 
from  the  lens  to  flame  and  image.     Find  the  ratio  between  the  dis- 
tances and  the  corresponding  dimensions,  and  compare  the  ratios. 

11.  Focus  a  spy-glass  or  small  telescope  on  an  object  a  mile  or  more 
distant.     The  rays  coming  from  the  object  to  the  eye  will  be  practi- 
cally parallel.     Place  a  lens,  the  focal  length  of  which  you  are  to 
measure,  in  front  of  the  telescope.     Paste  a  small-type  newspaper- 
clipping  on  a  piece  of  cardboard,  and  look  at  it  through  the  telescope 
and  lens.     Adjust  the  position  of  the  cardboard  so  that  the  printing 
appears  distinct.     Measure  the  distance  of  the  cardboard  from  the 
lens.     Obtain  the  average  of  several  such  trials.     Record  a  discussion 
of  the  proposition  that  this  average  distance  is  the  focal  length  of  the 
lens. 

12.  Provide  two  wooden  cubes  with  edges  about  4  cm.  long  and- 
with  the  grain  of  the  wood,  cut  in  each  block  a  groove  about  2  cm. 
deep  and  wide  enough  to  admit  the  edge  of  the  meter  rod  as  shown 
in  Fig.  272.     Provide  common  screws  so  that  the  blocks  may  be 
fixed  in  any  position  on  the  rod.     Provide  a  circular  biconvex  spec- 


366 


SCHOOL  PHYSICS. 


tacle-lens  having  a  known  focal  length  of  not  less  than  12  cm.  and  not 
more  than  16  cm.  Mount  this  lens  on  one  of  the  grooved  blocks,  e. 
It  may  be  held  in  place  between  slotted  brass  strips  each  fastened  to 
the  block  by  a  screw.  Upon  the  other  block,  mount  a  cardboard 
screen  about  8  cm.  square.  This  screen,  s,  may  be  carried  in  a  groove 
sawed  across  the  block,  a.  As  an  object  the  image  of  which  is  to  be 
projected  upon  the  screen,  cut  a  small  cross  in  the  varnish  on  the 
lamp-chimney  or  in  the  paper  cylinder  mentioned  in  Experiment  206. 
Give  the  top  of  the  cross  some  distinguishing  shape  or  mark  so  that 
you  can  tell  whether  its  image  is  erect  or  inverted.  Support  the  meter 
rod  horizontally  so  that  the  center  of  the  lens  shall  be  at  the  height 
of  the  center  of  the  cross,  and  so  that  m,  the  end  of  the  meter  rod, 
shall  be  just  under  the  cross.  Set  the  screen  at  a  distance  from  the 
cross  equal  to  about  three  times  the  focal  length  of  the  lens.  Slide 
the  lens  along  the  rod,  seeking  for  it  a  position  that  gives  upon  the 

screen  a  clear  image 
of  the  cross.  If  no 
such  position  for  the 
lens  can  be  found, 
move  the  screen  1  or 
2  cm.  further  from 
the  object,  and  renew 
the  search  for  the 
desired  position  of 
the  lens.  If  neces- 
sary, move  the  screen 
further  and  further 
from  the  object  until 
you  are  able  to  place  the  lens  so  that  a  distinct  image  is  obtained.  When 
it  is  found,  record  a  description  of  the  image,  as  erect  or  inverted,  and 
magnified,  diminished,  or  the  same  size.  Read  from  the  rod  the  dis- 
tance from  the  cross  to  the  lens,  and  enter  it  as  the  first  number  in 
a  second  column  headed  "  Object-distances."  Make  a  corresponding 
entry  of  the  distance  from  the  screen  to  the  lens  in  a  third  column 
headed  "Image-distances."  Without  changing  the  image-distance, 
try  to  secure  a  distinct  image  with  the  lens  in  any  other  position. 
If  you  can,  make  the  three  entries  as  before.  When  you  have 
exhausted  the  possibilities  of  object-distance  with  this  first  image- 
distance,  move  the  screen  10  cm.  further  from  the  cross,  secure  a  good 
image,  and  record  the  description  and  distances  as  before.  Move  the 


FIG.  272. 


REFRACTION  OF  RADIANT  ENERGY.  367 

screen  10  cm.  further  from  the  cross,  adjust  the  lens,  and  make  the 
record  as  before.  Continue  the  work  until  you  have  recorded  at  least 
five  pairs  of  distances.  Compare  your  results  with  those  of  Exercise 
11,  p.  364.  To  your  tabular-record,  add  a  fourth  column,  each 
entry  in  which  is  the  sum  of  the  two  recorded  distances.  Such  sums 
will  represent  the  distances  of  image  from  object.  Head  the  column 
"  Total  distances."  In  a  fifth  column,  enter  the  quotients  obtained 
by  dividing  the  several  total  distances  by  the  focal  length  of  the  lens. 
Try  to  get  a  quotient  as  small  as  3,  and  if  you  fail,  give  a  good  reason 
for  your  failure. 

Using  the  records  made  in  this  exercise,  test  the  accuracy  of  the 
statement  that  the  reciprocal  of  the  focal  length  equals  the  reciprocal 
of  the  object-distance  plus  the  reciprocal  of  the  image-distance,  or  of 
the  equivalent  statement  that  the  product  of  the  object  and  image 
distances  equals  the  sum  of  those  distances  multiplied  by  the  focal 
length. 

If  you  were  told  that  in  such  an  experiment  the  object-distance 
was  20  cm.  and  the  image-distance  60  cm.,  could  you  theoretically 
determine  any  other  object-distance  and  image-distance  for  the  same 
positions  of  object  and  screen? 

13.  In  similar  manner,  experimentally  determine  the  effect  that 
the  position  of   the  object  has   upon  the  character  of  the  images 
formed  by  a  concave  lens,  and  write  a  brief  discussion  of  the  results 
attained. 

14.  Focus  a  magnifying  glass  on  a  finely  divided  decimeter  scale. 
Hold  a  similar  scale  at  the  distance  of  distinct  vision  (about  25  cm.). 
With  one  eye,  look  through  the  lens  at  the  first  scale  and  with  the 
other  eye  look  directly  at  the  other  scale.    By  continued  trial,  the  eyes 
will  become  accustomed  to  the  unusual  conditions,  and  the  two  images 
will  appear  as  if  one  was  superposed  on  the  other.     Then  count  how 
many  divisions  of  the  magnified  scale  correspond  to  a  certain  number 
of  divisions  of  the  other  scale.     Divide  the  latter  number  by  the 
former  to  determine  the  magnifying  power  of  the  lens. 

15.  Determine  the  focal  distance  of  the  lens  used  in  Exercise  14 
and  call  it  f.     Call  the  distance  taken  in  that  exercise  as  the  distance 

of  distinct  vision,  v.  Determine  the  value  of  --f  1  and  compare  it 
with  the  magnifying  power  of  the  lens  as  determined  in  Exercise  14. 


868  SCHOOL  PHYSICS. 

V.    SPECTKA,   CHROMATICS,  ETC. 
Analysis. 

Experiment  242.  —  Admit  a  sunbeam  through  a  small  opening  in 
the  shutter  of  a  darkened  room.  In  the  path  of  the  beam,  place  a 
prism,  as  shown  in  Fig.  273.  Instead  of  the  colorless  image  of  the 


FIG.  273. 

sun  at  E,  there  appears  upon  the  white  screen  a  many-colored  band 
changing  gradually  from  red  at  the  lower  end,  through  all  the  colors 
of  the  rainbow,  to  violet  at  the  upper  end. 

Experiment  243.  —  Paste  a  strip  of  white  paper  3  x  0.2  cm.  upon  a 
black  card.  Upon  a  similar  card,  paste,  end  to  end,  strips  of  red,  of 
white,  and  of  blue  paper,  each  1  x  0.2  cm.  In  a  well-lighted  room, 
place  the  first  card  with  the  white  strip  vertical.  Hold  a  prism  with 
its  refracting  edges  vertical,  and  look  through  it  at  the  white  strip. 
On  its  way  to  the  eye,  the  beam  of  white  light  from  the  strip  will  be 
separated  into  differently  colored  parts.  You  will  see  a  colored  band 
instead  of  the  white  strip.  Similarly,  view  the  tri-color  strip  on  the 
other  card,  and  carefully  compare  the  three  colored  bands  that  cor- 
respond to  the  three  parts  of  the  strip. 

295.  Dispersion.  —  The  separation  of  differently  colored 
rays  by  refraction  is  called  dispersion.  Experiment  242 
shows  that  white  or  colorless  light,  like  that  of  the  sun,  is 


SPECTRA,   CHROMATICS,   ETC.  369 

a  mixture  of  radiations  of  varying  color  and  refrangi- 
bility.  The  differences  in  deviation  arise  from  differ- 
ences of  wave-length,  the  angle  of  deviation  increasing 
as  the  wave-length  diminishes. 

296.  Spectra. —  The  many-colored  image  of  the  sun  pro- 
jected on  the  screen  in  Experiment  242  is  called  a  spectrum. 
It  is  called  a  solar  spectrum  when  the  source  of  light  is 
under  consideration,  and  a  prismatic  spectrum  when  the 
method  of  producing  it  is  under  consideration.  Most  in- 
candescent bodies  emit  light  of  varying  wave-length  and 
refrangibility. 

(a)  These  prismatic  colors  are  generally  described  as  violet,  in- 
digo, blue,  green,  yellow,  orange,  and  red.  The  initial  letters  of 
these  terms  form  the  meaningless,  mnemonic  word  "vibgyor." 


FIG.  274. 

In  fact,  the  gradations  of  color  are  imperceptible.  The  differently 
colored  images  of  the  sun  overlap,  as  shown  in  Fig.  274.  Conse- 
quently, such  an  opening  in  the  shutter  gives  an  impure  spectrum. 

Synthesis. 

Experiment  244.  — Repeat  Experiment  242,  and  hold  a  second  prism 
in  a  reversed  position  close  behind  the  first.  The  light  dispersed  by 
the  first  prism  will  be  reunited  by  the  second,  and  emerge  as  colorless 
light.  The  two  prisms  have  the  effect  of  a  plate  with  its  refracting 
faces  parallel. 

Experiment  245.  —  Let  light  that  has  been  dispersed  by  a  prism  fall 
upon  an  achromatic  convex  lens  as  shown  in  Fig.  275.     It  will  be  re- 
fracted to  a  focus  and  recombined  to  form  white  light.     Hold  a  card 
24 


370 


SCHOOL   PHYSICS. 


between  the  prism  and  the  lens  so  as  to  cut  off  the  red  light  and 
notice  the  focus  of  what  remains.     Similarly  cut  off  the  violet  light, 


FIG.  275. 

and  again  notice  the  focus  of  what  remains.  A  concave  mirror  may 
be  used  to  reflect  the  light  to  a  focus  instead  of  using  the  lens  as 
above  described. 

Experiment  246.  —  Make  a  "Newton  disk,"  painting  the  prismatic 
colors  in  proper  proportion  as  indicated  by  Fig.  276,  or  pasting  sectors 
of  properly  colored  paper 
upon  cardboard.  Tt  is  bet- 
ter to  divide  the  surface 
given  to  each  color  into 
smaller  sectors  arranged 
alternately  as  shown  in 
Fig.  277.  Fasten  this  disk 
to  a  large  top,  or  to  a 
whirling  table,  and  cause 
it  to  revolve  rapidly.  The 
1  blends  the  colors,  and  the  disk  appears  grayish 


FIG.  276. 


FIG.  277. 


"  persistence  of  vision 

white. 

Disks  about  15  or  20  cm.  in  diameter  may  be  cut  from  colored 

paper,  and  a  hole  cut  at  the  center  of  each  of  such  size  that  the  disks 

may  be  slipped  over  the  spindle  of  the 
whirling  table.  By  cutting  each  along 
a  radial  line,  the  several  disks  may 
be  worked  into  each  other  as  shown  in 
Fig.  278,  and  in  such  a  way  as  to  expose 
the  several  colors  to  view  in  any  desired 
FIG.  278.  proportion. 


SPECTRA,   CHROMATICS,   ETC.  371 

Experiment  247.  —  Hold  a  hand  mirror  near  the  dispersing  prism 
so  as  to  reflect  the  refracted  light  to  a  distant  wall  or  ceiling.  Give  a 
rapid,  angular  motion  to  the  mirror  so  that  the  spectrum  moves  to 
and  fro  very  quickly  in  the  direction  of  its  length.  The  spectrum 
changes  to  a  band  of  white  light  with  a  colored  spot  at  each  end. 

297.  The  Composition  of  White  Light.  —  We  have  now 
shown,  by  both  analysis  and  synthesis,  that  white  light  is 
composed  of  the  prismatic  colors.     We   have   decomposed 
white  light  into  its   constituents,  and  recombined  these 
constituents  into  white  light. 

Experiment  248.  —  With  a  double-convex  lens  in  a  darkened  room 
project  on  the  screen  an  image  of  the  aperture  in  the  shutter.  The 
white  image  will  be  fringed  with  color. 

298.  Chromatic  Aberration.  —  Because  of  their  greater 
refrangibility,  the  focus  of  the  violet  rays  is  nearer  the 
lens  than  the  focus  of  the  red  rays, 

as  illustrated  in  Fig.  279.  If  the 
screen  is  as  near  the  lens  as  the 
focus  marked  v,  the  outer  fringe  is 

j        .j.    ,1  .  (.        -  FIG.  279. 

red ;   if  the  screen  is  as  far  from 

the  lens  as  the  focus  marked  r,  the  outer  fringe  is  violet. 
This  difference  in  the  deviation  of  differently  colored  rays 
is  called  chromatic  aberration. 

(a)  A  double-convex  lens  of  crown-glass  may  be  combined  with  a 
plano-concave  lens  of  flint-glass  so  as  to  overcome  the  dis- 
/v\  persive  effect  for  some  of  the  colors  without  overcoming 

/  \  i  the  converging  effect.  As  such  a  compound  lens  forms 
an  image  that  is  nearly  free  from  the  fringe  of  spectral 
colors,  it  is  called  an  achromatic  lens. 


Experiment  249.  —  Gradually  raise  the  temperature  of 
FIG.  280.     a  piatinum  wire  by  an  electric  current.     The  first  radia- 
tions emitted  are  those  of  "  obscure  heat " ;  i.e.,  they  affect  the  nerves 


372  SCHOOL  PHYSICS. 

of  general  sensation  only.  The  vibrations  increase  in  frequency  and 
amplitude  with  the  temperature,  and,  at  about  525°,  the  eye  perceives 
the  wire  as  a  dark  red  line.  As  the  temperature  continues  to  rise, 
waves  of  shorter  and  shorter  wave-length  are  added,  while  those 
previously  emitted  are  increased  in  amplitude.  The  wire  succes- 
sively appears  orange  and  yellow  and  then  becomes  white  hot,  the 
light  emitted  being  exceedingly  complex. 

299.  Color  is  a  property  of  light,  and  depends  upon  wave- 
length. Thus,  the  relation  between  color  and  light  is  the 
same  as  that  between  pitch  and  sound. 

(a)  The  wave-lengths  that  correspond  to  the  several  prismatic 
colors  as  they  appear  in  the  solar  spectrum  are  as  follows  :  — 


Violet,  4,059 

Indigo  (violet-blue),  4,383 


Green,  5,271 
Yellow,  5,808 


Orange,  5,972 
Red,       7,000 


Blue  (cyan-),  4,960 

These  magnitudes  are  for  the  middle  points  of  the  several  colors,  and 
represent  ten-millionths  of  a  millimeter.  Light  of  only  one  wave- 
length is  said  to  be  monochromatic  or  homogeneous. 

(&)  An  incandescent  body  emits  light  with  wave-lengths  that  grade 
imperceptibly  from  values  less  to  values  greater  than  any  of  those 
given  above.  When  the  wave-lengths  are  much  less  or  greater  than 
those  above  given,  the  radiation  is  incapable  of  exciting  vision. 
Within  the  limits  of  visibility  are  an  indefinitely  great  number  of 
wave-lengths,  and  a  correspondingly  great  number  of  colors.  When 
light  of  all  grades  of  refrangibility  within  these  limits  is  blended,  as 
it  is  in  sunlight,  the  resultant  effect  is  white  or  colorless  light.  When 
the  light  that  corresponds  to  some  of  the  prismatic  colors  is  wanting, 
the  resultant  effect  of  blending  what  is  present  is  colored  light. 
Many  artificial  lights  are  deficient  in  some  of  these  wave-lengths. 

(c)  Since  the  wave-length  for  the  extreme  red  is  approximately 
twice  that  of  the  extreme  violet,  it  may  be  said  that  the  range  of  the 
visible  spectrum  is  only  about  one  octave.  The  full  spectrum,  from 
the  extreme  ultra-violet  to  the  longest  waves  yet  recognized,  embraces 
more  than  seven  octaves.  These  invisible  spectra  have  been  explored 
with  delicate  thermoscopes  and  by  photography.  Wave-lengths  twenty 
times  that  of  the  visible  red,  and  corresponding  to  the  temperature  of 
melting  ice,  have  thus  been  detected  in  the  radiation  of  the  surface  of 


SPECTRA,    CHROMATICS,   ETC.  373 

the  moon.     The  method  of  phosphorescence  is  also  employed,  while 
fluorescence  is  made  use  of  in  studying  the  ultra-violet  region. 

(of)  Every  sensation  of  light  that  the  human  eye  experiences  is  the 
effect  of  impressing  about  five  hundred  trillion  (5  x  1014)  waves  upon 
the  ether  each  second.  If  the  frequency  of  the  ether  waves  is  much 
lower,  the  result  is  chiefly  heat. 

Color  of  Bodies. 

Experiment  250.  —  Repeat  Experiment  242,  and  hold  a  piece  of  deep 
red  glass  between  the  slit  in  the  shutter  and  the  prism.  Notice  that 
the  intensity  of  illumination  is  reduced  less  in  the  red  than  in  any 
other  part  of  the  spectrum. 

Experiment  251.  —  Paste  three  strips  of  paper,  one  white,  one 
vermilion-red,  and  one  aniline-violet,  each  about  3  x  0.2  cm.,  upon 
sheets  of  black  cardboard.  Successively  place  these  strips  in  a  strong 
light,  and  look  at  them  through  a  prism  held  with  its  refracting  edge 
parallel  to  the  length  of  the  strips.  Carefully  compare  the  coloring 
of  the  images  of  the  three  strips  thus  viewed. 

Experiment  252.  —  Paint  three  narrow  strips  of  cardboard,  one 
vermilion-red,  one  emerald-green,  and  the  other  aniline-violet.  Be 
sure  that  the  coats  are  thick  enough  thoroughly  to  hide  the  card- 
board. When  dry,  hold  the  red  strip  in  the  red  of  the  solar  spectrum ; 
it  appears  red.  Move  it  slowly  through  the  orange  and  yellow ;  it 
grows  gradually  darker.  In  the  green  and  colors  beyond,  it  appears 
black.  Repeat  the  experiment  with  the  other  two  strips,  and  carefully 
notice  the  effects. 

Experiment  253.  — Make  a  loosely  wound  ball  of  candle-wick ;  soak 
it  in  a  strong  solution  of  common  salt  in  water ;  squeeze  most  of  the 
brine  out  of  the  ball ;  place  the  ball  in  a  plate,  and  pour  alcohol  over 
it.  Take  it  into  a  dark  room  and  ignite  it.  Examine  objects  of 
different  colors,  as  strips  of  ribbon  or  cloth,  by  this  yellow  light. 
Only  yellow  objects  will  have  their  usual  appearance. 

Experiment  254.  —  In  a  clear  tumbler  or  large  beaker  of  water, 
dissolve  a  little  white  castile  soap,  or  stir  a  few  drops  of  an  alcoholic 
solution  of  mastic.  Hold  the  vessel  in  the  hand,  and  examine  the 
liquid  by  transmitted  sunlight.  Notice  that  it  appears  yellowish-red. 
In  a  small  test-tube,  either  liquid  will  appear  colorless.  Place  a  black 


374  SCHOOL  PHYSICS. 

screen  behind  the  vessel  and  examine  the  liquid  by  reflected  sunlight. 
Notice  that  it  appears  blue. 

300.  The  Color  of  a  Body  depends  upon  the  light  that 
the  body  reflects  or  transmits  to  the  eye.  The  color  of  the 
light  thus  sent  to  the  eye  depends  partly  upon  the  nature 
of  the  incident  light,  and  partly  upon  the  nature  of  the 
body.  Some  bodies  have  a  power  that  may  be  described 
as  selective  absorption,  reflecting  or  transmitting  light  of 
certain  wave-lengths,  and  absorbing  the  others.  When 
a  house  is  painted  yellow,  the  painters  lay  on  not  a  yel- 
low color  but  a  substance  that  absorbs  from  sunlight  all 
the  colors  except  yellow.  If  the  light  incident  upon  a 
body  has  only  the  wave-lengths  that  the  body  absorbs, 
the  body  can  send  no  light  to  the  eye  and,  therefore, 
appears  black. 

(a)  A  red  ribbon  is  red  because  it  reflects  light  of  the  particular 
wave-length  that  corresponds  to  the  sensation  of  redness,  and  absorbs 
the  rest.  A  white  ribbon  is  white  because  it  reflects  the  same  propor- 
tion of  all  the  light  that  constitutes  sunlight.  A  piece  of  blue  glass 
is  blue  because  it  transmits  or  reflects  light  of  the  particular  wave- 
length that  corresponds  to  the  sensation  of  blueness,  and  absorbs  the 
rest.  Glass  that  absorbs  none  of  the  incident  light  is  colorless. 

(&)  The  earth's  atmosphere  freely  transmits  yellow  and  red  light, 
and  freely  reflects  blue  light  after  the  manner  of  the  solutions  used  in 
Experiment  254.  The  blue  of  the  sky  is  due  to  light  thus  reflected. 
When  the  sun  is  near  the  horizon,  its  light  traverses  a  thicker  layer 
of  air  than  it  does  at  noon.  Hence  the  predominance  of  yellow  and 
red  in  the  light  of  the  morning  and  evening  hours. 

Complementary  Colors. 

Experiment  255.  —  Repeat  Experiment  246,  and  receive  the  red  and 
orange  light  upon  a  prism  of  small  refracting  angle  placed  behind 
the  lens.  The  prism  will  deflect  the  red  and  orange,  and  form  a 
reddish  colored  image  at  n.  The  violet,  indigo,  blue,  green,  and 


SPECTRA,    CHROMATICS,    ETC. 


875 


FIG.  282. 


yellow  light,  not  caught  by  the  prism,  will  unite  at  /  to  form  a 
greenish  image.  When  the  prism  is  removed,  the  reddish  light  that 
fell  at  n,  and  the  greenish 
light  that  fell  at  /,  unite  to 
form  white  light.  By  shifting 
the  position  of  the  prism,  other 
parts  of  the  beam  may  be  de- 
flected to  the  side,  giving  rise 
to  various  pairs  of  colors,  as 
orange  and  blue,  etc.  Each  of  these  pairs  of  colors  has  this  property 
in  common,  that  when  united  they  form  white  light. 

Experiment  256.  —  Again  repeat  Experiment  246,  holding  a  paper 

screen  in  front  of  the  lens. 
Mark  the  positions  of  the  yel- 
low and  blue  parts  of  the  spec- 
trum on  the  paper,  and  cut 
narrow  slits  across  the  spec- 
trum so  as  to  allow  the  yellow 
and  the  blue  light  to  pass 

through  the  lens.  These  two  simple  colors  will  be  blended  by  the 
lens,  forming  a  light  that  is  nearly  white.  The  effect  of  mingling 
any  two  colors  may  be  determined  in  this  way. 

Experiment  257.  —  Lay  a  piece  of  blue  paper  and  a  piece  of  yellow 
paper,  each  about  5  cm.  square, jiipon  a  black  horizontal  surface  and 
about  5  cm.  apart.  Hold  a  piece  of  plate  glass  10  or  15  cm.  above 
the  colored  papers  and  in  a  vertical  plane  that  passes  between  them. 
Looking  obliquely  downward,  you  may  see  one  of  the  papers  by  light 
that  the  glass  transmits,  and  an  image  of  the  other  paper  by  light  that 
the  glass  reflects.  By  trial,  you  can  find  positions  for  the  glass  and 
eye  such  that  the  object  seen  by  the  transmitted  light  and  the  image 
produced  by  the  reflected  light  overlap  each  other  with  a  blending  of 
their  colors. 

301.  Complementary  Colors  are  any  two  colors  the 
blending  of  which  produces  ivhite  light.  If  all  the  colors 
of  the  solar  spectrum  are  divided  into  two  parts  and  the 
colors  in  each  part  are  blended,  each  resultant  color  evi- 


376 


SCHOOL  PHYSICS. 


FIG.  283. 


dently  has  what  the  other  needs  to  make  white  light. 
Either  of  such  colors  is  said  to  be  complementary  to  the 
other.  When  complementary  colors  are  placed  in  prox- 
imity, each  heightens  the  effect  of  the  other,  by  contrast. 

(a)  Any  two  colors  standing  opposite  each  other  in  Fig.  283  are 
complementary  to  each  other.  If  such 
colors  are  blended,  the  resultant  is  white 
light;  if  any  two  alternate  colors  are 
blended,  the  resultant  will  be  the  color 
that  appears  between  them  in  the  figure. 

Experiment  258.  —  Cut  holes  8  cm.  in 
diameter  at  the  middle  of  two  boards 
each  18  x  10  cm.  and,  in  each  case,  re- 
move part  of  the  strip  remaining  at 
the  middle  of  one  of  the  long  edges. 
Thinly  coat  the  circular  edges  with 
melted  beeswax  or  paraffine.  Provide 
four  pieces  of  clear  window  glass,  10  x  18  cm.,  and  fasten  one  of  them 
with  marine  glue  to  each  side  of  each  board,  thus  covering  the  open- 
ings. The  glue  and  the  surfaces  to  be  joined  should  be  heated.  The 
glue  may  be  thinned,  if  necessary,  with  naphtha.  Fill  one  of  these 
"  chemical  tanks  "  with  a  solution  of  copper  sulphate,  and  the  other 
with  a  solution  of  potassium  dichromate.  Kepeat  Experiment  242, 
and  hold  the  yellow  solution  between  the  shutter  and  the  prism. 
Notice  that  the  solution  absorbs  the  radiations  of  shorter  wave-length 
and  thus  cuts  the  violet,  indigo  and  blue  from  the  spectrum.  Change 
the  tanks,  and  notice  that  the  blue  solution  absorbs  the  radiations  of 
greater  wave-length  and  thus  cuts  the  yellow,  orange  and  red  from 
the  spectrum.  If  both  solutions  are  interposed,  the  green  alone  will 
be  freely  transmitted. 

Experiment  259.  —  With  a  yellow-colored  crayon,  draw  a  broad 
mark  on  the  blackboard.  Along  the  same  line,  draw  a  similar  mark 
with  a  blue  crayon.  Also  mix  a  small  quantity  of  chrome-yellow 
with  a  like  quantity  of  some  ultramarine-blue  pigment.  The  blend- 
ing of  the  blue  and  the  yellow  colors  in  Experiment  256,  gave  a 
white;  the  blending  of  the  yellow  and  the  blue  pigments  gives  a 
green. 


SPECTRA,    CHROMATICS,    ETC.  377 

302.  Mixing  Pigments  is  a  very  different  thing  from 
mixing  colors,  as  has  just  been  illustrated.     In  the  ma- 
jority of  cases,  the  scattering  of  incident  light  takes  place 
not  only  at  the  surface  of  bodies  but  also  at  distances 
below  the  surface.     This  distance  is  generally  small  but 
in  some  cases  it  is  considerable.      When  sunlight  falls 
obliquely  upon  a  piece  of  blue  glass,  part  of  the  incident 
light  is  reflected  at  the  anterior  surface  of  the  glass ;  the 
color  of  this  reflected  light  is  white.     Another  part  of 
the  incident  light  is  reflected  from  the  posterior  surface  ; 
the  color  of  this  light  that  has  twice  traversed  the  thick- 
ness of  the  glass  is  blue,  the  radiations  of  other  wave- 
lengths having  been   absorbed.      The  difference  in  the 
colors  may  be  seen  by  receiving  the  reflected  light  upon  a 
screen.     In  the  case  of  pigments,  most  of  the  scattered 
light  comes  from  below  the  surface.     In  Experiment  259, 
the  yellow  pigment  removed  most  of  the  violet,  indigo 
and  blue  by  such  absorption.     The  blue  pigment  similarly 
removed  most  of  the  yellow,  orange  and  red.     (Compare 
Experiment  258.)    The  radiations  that  escaped  both  were 
of  the  particular  wave-length  that  constitutes  green  :  — 

ffl&tt- 

Experiment  260.  —  Fill  the  bulb  of  an  air  thermometer  with  clear 
water.  Cut  a  circular  opening  (somewhat  smaller  than  the  bulb)  in 
a  large  sheet  of  cardboard.  Reflect  a  sunbeam  into  a  darkened  room 
so  that  it  shall  pass  through  the  opening  in  the  cardboard  and  fall 
upon  the  water-filled  bulb.  Adjust  the  position  of  the  bulb  until 
circular  spectra  are  thrown  by  the  bulb  back  upon  the  cardboard 
screen. 

303.  A  Rainbow  is  a  solar  spectrum  formed  by  water- 
drops.     The  necessary  conditions  are  :  — 


378 


SCHOOL  PHYSICS. 


(1)  A  shower  during  sunshine. 

(2)  That  the  observer  shall  stand  with  his  back  to  the 
sun,  and  facing  the  falling  drops. 

(a)  The  center  of  the  circle  of  which  the  rainbow  forms  a  part  .is 
in  the  prolongation  of  a  line  drawn  from  the  sun  through  the  eye  of 
the  observer.     This  line  is  called  the  axis  of  the  bow. 

(b)  Often,  a  second  bow  is  visible.     The  inner  or  primary  bow  is 
much  brighter  than  the  other;  the  outer  or  secondary  bow  has  the 
order  of  colors  reversed,  as  indicated  in  Fig.  284. 

(c)  The  rays  of  sunlight  incident  upon  the  rain-drops  are  refracted 
as  they  enter  the  drop,  internally  reflected,  and  chromatically  dis- 
persed, as  illustrated  in  Experiment  260.     The  drop  at  V  has  an  angu- 
lar distance  of  40°  from  EO,  the  axis  of  the  bow,  and  sends  violet 
rays  to  the  eye  at  E,  and  red  rays  below  the  eye.     Other  drops,  at  the 

same  angular  distance  from  EO,  send  vio- 
let light  to  the  eye  and,  therefore,  form  a 
violet-colored  circular  arc  of  which  0  V  is 
the  radius  of  curvature.  Similarly,  the 
angle  of  deviation  for  red  rays  is  such 
that  the  drop,  R,  at  an  angular  distance 
of  42°  from  EO,  sends  red  rays  to  the  eye 
of  the  observer  and  violet  rays  above  the 
eye.  Other  drops  at  the  same  angular  dis- 
tance send  red  light  to  the  eye  and,  there- 
fore, form  a  red-colored  circular  arc,  of 
which  OR  is  the  radius  of  curvature.  The  primary  bow,  therefore, 
has  an  angular  width  of  2°,  the  other  prismatic  colors  ranging  in 
regular  order  between  the  violet  and  the  red. 

(d)  The  secondary  bow  involves  two  reflections  within  the  rain- 
drops, as  shown  at  r  and  v.     The  drops  that  send  these  rays  to  the  eye 
are  at  the  angular  distances  of  51°  and  54°  respectively  from  EO.     As 
some  light  is  lost  at  each  reflection,  the  secondary  bow  is  fainter  than 
the  primary. 

Pure  Spectra. 

Experiment  261.  —  Cut  a  very  narrow  slit,  2  or  3  cm.  long,  in  a  piece 
of  tin  or  of  tin-foil,  and  fasten  the  sheet  over  the  opening  in  the  shutter 
of  a  darkened  room  so  that  the  slit  shall  be  horizontal.  Hold  a  prism 
about  1.5  m.  from  the  slit  and  with  its  edges  horizontal.  Looking 


FIG.  284. 


SPECTRA,    CHROMATICS,   ETC. 


379 


through  the  prism  at  the  slit,  turn  the  prism  about  its  axis  until  the 
colored  image  of  the  slit  is  at  the  least  angular  distance  from  the  slit 
itself.  The  colors  of  the  image  will  show  with  a  greater  distinctness 
than  before  observed. 

Experiment  262.  —  Change  the  position  of  the  tin-foil  used  in  Ex- 
periment 261,  so  that  the  slit  shall  be  vertical.  Using  a  convex  lens 
with  a  focal  distance  of  about  30  cm.,  project  an  image  of  the  slit  upon 
a  white  screen  at  a  considerable  distance.  Place  a  glass  or  a  carbon 
disulphide  prism  near  the  lens,  and  between  it  and  the  screen.  See 
that  its  edges  are  vertical,  and  that  it  is  properly  placed  for  mini- 
mum deviation.  Shift  the  position  of  the  screen  so  that  the  rays  from 
the  prism  fall  normally  upon  it,  but  keeping  it  at  the  same  distance 
from  the  lens.  The  spectrum  visible  upon  the  screen  will  be  more 
distinct  than  any  before  observed. 

304.  A  Pure  Spectrum  is  made  up  of  a  succession  of 
colored  images  with  little  or  no  overlapping.  The  first 
requisite  in  preventing  the  overlapping,  like  that  of  the 
impure  spectrum  described  in  §  296  (a),  is  that  the  slit 
be  very  narrow. 

(a)  A  spectroscope  is  an  instrument  used  to  produce  a  spectrum  of 
the  light  from  any  source,  and  for  its  study.  It  affords  a  delicate 
means  of  chemical 
analysis  and  is  one  of 
the  most  powerful 
aids  to  modern 
science.  In  one  of  its 
simple  forms  it  con- 
sists of,  — 

(1)  A    collimator, 
C,  a  tube  with  an  ad- 
justable slit  with  par- 
allel edges  at  the  outer 
end  through  which  the 
light  enters,  and  at  the 

other  end  a  collimating  lens  that  brings  the  rays  into  a  parallel  beam. 

(2)  A  prism,  P,  or  a  series  of  prisms,  that  receives  the  radiation 
from  C,  and  disperses  it,  thus  forming  a  spectrum. 


FIG.  285. 


380  SCHOOL  PHYSICS. 

(3)  A  telescope,  jT,  through  which  the  magnified  image  of  the  spec- 
trum is  viewed.  The  spectrum  is  received  directly  upon  the  retina  of 
the  eye  and  may  be  distinctly  seen  even  when  the  radiation  is  feeble. 

It  is  often  necessary  to  determine  the  position  of  certain  lines  that 
appear  in  the  spectrum  (§  307).  In  such  cases,  the  spectroscope  is 
provided  with  a  third  tube  that  carries  a  collimatinglens,  and  a  trans- 
parent plate  on  which  a  fine  scale  has  been  engraved.  Light,  as  from 
a  candle,  enters  the  outer  end  of  this  tube,  passes  from  the  collimat- 
ing  lens  at  the  inner  end,  and  is  reflected  from  the  face  of  the  prism 
so  that  it  enters  the  telescope  with  the  light  that  is  being  examined. 
Thus  the  spectrum  and  the  image  of  the  scale  are  viewed  simultane- 
ously and  in  close  juxtaposition. 

A  pocket  form  of  the  spectroscope,  often  called  a  direct-vision 
spectroscope,  has  two  telescoping  tubes.  The  inner  tube  carries  a 
series  of  three  or  more  prisms  made  of  different  kinds  of  glass,  and 
so  placed  as  to  overcome  the  deviation  of  the  light  from  a  straight 
path  and  yet  to  preserve  the  dispersion.  The  outer  tube  carries  an 
adjustable  slit  for  the  admission  of  light  which,  after  dispersion,  is 
received  by  the  eye  at  the  other  end  of  the  instrument.  Such  an  in- 
strument is  not  very  expensive,  and  may  be  made  to  answer  for  the 
purposes  of  this  book. 

Spectrum  Analysis. 

Experiment  263.  —  Examine  a  candle-flame  with  a  spectroscope,  and 
notice  that  the  colored  spectrum  is  continuous  through  all  the 
prismatic  colors.  Evidently,  the  radiation  is  extremely  complex. 

Experiment  264.  —  Dip  a  platinum  wire  or  a  strip  of  asbestos  into 
a  solution  of  sodium  chloride  (common  salt),  and  hold  it  in  the  almost 
colorless  flame  of  a  Bunsen  burner.  The  sodium  vapor  colors  the 
flame  yellow.  Examine  this  sodium  flame  with  a  spectroscope,  and 
notice  that  the  spectrum  consists  of  a  bright  yellow  line  instead  of 
the  continuous  multi-colored  band.  If  your  spectroscope  was  of  high 
dispersive  power,  it  would  show  that  the  sodium  line  is  really  double. 
These  two  fine  lines  represent  wave-frequencies  of  508.3  x  1012  and 
509.3  x  1012  respectively.  If  the  flame  is  similarly  colored  with  a 
solution  of  chloride  of  lithium,  the  bright  line  spectrum  will  have 
a  carmine  color.  If  the  flame  is  colored  with  strontium  nitrate,  the 
crimson  flame  will  yield  a  spectrum  composed  of  bright  lines  the 
colors  and  positions  of  which  are  different  from  those  of  either  of 
the  spectra  previously  examined.  If  the  flame  is  colored  with  a  mix- 


SPECTRA,   CHROMATICS,   ETC.  381 

ture  of  these  three  substances,  the  spectrum  will  show  all  of  the  bright 
lines  previously  observed. 

305.  Spectrum  Analysis.  —  It  has  long  been  known  that 
when  certain  substances  are  heated  they  give  colored 
flames,  the  yellow  of  sodium,  the  lilac  of  potassium,  etc., 
being  familiar.  Each  of  the  chemical  compounds  used  in 
Experiment  264  has  a  metallic  base,  sodium,  lithium,  or 
strontium.  The  vapors  of  these  metals  yielded  the  spec- 
tra observed.  Like  tuning-forks,  free  molecules  have 
definite  vibration-periods;  e.g.,  the  ether  waves  set  up 
by  incandescent  sodium  have  the  same  frequency  whether 
the  sodium  is  solar,  stellar  or  terrestrial.  The  character- 
istic frequency  of  the  radiation  thus  established  deter- 
mines the  relative  position  of  the  corresponding  spectrum. 
As  the  spectra  of  such  substances  are  characteristic,  i.e., 
no  two  of  them  are  alike,  they  may  be  used  for  the  identi- 
fication of  the  several  substances  that  produce  them. 
This  method  of  analyzing  composite  radiations,  or  of  iden- 
tifying substances  by  the  spectra  of  their  incandescent  vapors, 
is  catted  spectrum  analysis. 

(a)  As  a  condition  necessary  for  the  production  of  the  spectrum, 
the  temperature  must  be  so  high  that  the  substance  to  be  examined 
may  be  vaporized,  disassociated,  and  made  incandescent.  If  a  com- 
pound gas  or  vapor  is  not  disassociated  at  the  temperature  employed, 
it  gives  its  own  spectrum  instead  of  the  spectra  of  its  constituent 
elements.  Having  mapped  the  spectra  of  all  known  substances,  the 
presence  of  new  lines  in  any  spectrum  would  indicate  the  presence  of 
a  substance  previously  unknown.  The  quantity  of  material  required 
for  such  examination  is  exceedingly  small,  a  hundred-millionth  of  a 
milligram  of  strontium  giving  the  spectrum  characteristic  of  that 
element.  The  chemist  is  thus  provided  with  a  method  of  qualita- 
tive analysis  of  far  greater  power  than  any  previously  known.  By  it, 
the  chemistry  of  the  stars  has  been  studied,  and  the  extreme  gen- 
erality of  the  diffusion  of  the  elements  in  nature  has  been  shown, 


382  SCHOOL  PHYSICS. 

and  several  new  elements  have  been  discovered.      The  method  has 
been  successfully  applied  in  the  industrial  arts. 

Experiment  265.  —  Remove  the  objective  from  an  optical  lantern 
(§  323).  From  the  lantern,  send  a  beam  of  electric  or  calcium  light 
through  a  narrow  vertical  slit  in  a  tin  screen.  Beyond  the  screen, 
place  a  double  convex  lens  to  receive  the  light  that  passes  through  the 
slit.  Beyond  the  lens,  place  a  prism  so  as  to  throw  a  spectrum  on  a 
screen  still  beyond.  Place  a  Bunsen  burner  or  an  alcohol  lamp  be- 
tween the  lantern  and  the  slit  and,  in  its  almost  colorless  flame,  hold  a 
bit  of  sodium.  The  metal  will  burn  giving  an  intense  yellow  to  the 
flame.  Notice  that  the  yellow  of  the  spectrum,  instead  of  being  more 
intensely  illuminated,  is  marked  by  a  dark  band.  Then  hold  a  piece 
of  tin  between  the  lantern  and  the  flame  and  so  as  to  cut  off  the  light 
of  the  lantern  from  the  upper  part  of  the  slit.  The  upper  part  of  the 
slit  is  now  traversed  by  light  from  the  sodium-colored  flarne,  and 
the  lower  part  of  the  slit  by  light  from  both  the  lantern  and  the 
flame.  The  image  of  the  slit  is  inverted,  and  two  parallel  spectra  are 
thrown  on  the  screen.  One  of  these  is  the  bright-line  spectrum  of 
sodium ;  the  other  shows  a  dark  line  on  a  continuous  spectrum. 
Notice  that  the  bright  line  of  one  spectrum  falls  in  the  same  relative 
position  as  the  dark  line  of  the  other  spectrum. 

Experiment  266.  —  Place  some  common  salt  on  the  wick  of  an 
alcohol  lamp.  The  sodium  of  the  salfr  will  give  a  yellow  tinge  to  the 
flame.  Let  a  beam  of  electric  or  calcium  light  pass  through  this 
yellow  flame  and  fall  upon  the  collimator  slit  of  the  spectroscope ; 
study  its  spectrum.  A  dark  line  crosses  the  spectrum,  which  thus  be- 
comes discontinuous.  Shut  off  the  lantern  light,  and  the  sodium 
flame  again  gives  its  bright-line  spectrum  as  before.  Turn  on  the 
lantern  light,  and  remove  the  sodium-colored  flame.  Notice  that  the 
spectrum  is  continuous.  Replace  the  sodium  flame,  and  notice  that 
the  dark  line  of  the  discontinuous  spectrum  falls  in  the  same  rela- 
tive position  as  the  bright  line  of  the  sodium  spectrum,  just  as  if  the 
sodium  vapor  absorbed  light  of  the  same  refrangibility  as  that  it  emits. 

306.  Kinds  of  Spectra.  —  From  the  foregoing,  it  appears 
that  a  spectrum  may  be  continuous  or  discontinuous,  and 
that  a  discontinuous  spectrum  may  be  a  bright-line  spec- 
trum or  a  dark-line  spectrum.  For  obvious  reasons, 


UNIVERSITY  OF  CALIFORNIA 


dark-line  spectra  are  sometimes  called  reversed  spectra,  or 
absorption  spectra. 

307.  The  Fraunhofer  Lines.  —  A  spectrum  of  sunlight 
is  crossed  by  dark  lines,  many  hundreds  of  which  have 
been  counted  and 
accurately  mapped. 


The  more  conspic- 
uous of  these  dark 
v  ..  ,.  FIG.  286. 

lines  are  distin- 
guished by  letters  of  the  alphabet,  as  shown  in  Fig.  286. 
A  few  of  these  dark  lines  in  the  solar  spectrum  are  due 
to  absorption  in  the  earth's  atmosphere,  but  by  far  the 
greater  number  originate  in  the  selective  absorption  of 
the  solar  atmosphere  itself. 

(a)  In  accordance  with  the  principles  illustrated  by  the  experiments 
immediately  preceding,  and  as  more  fully  explained  in  the  paragraph 
immediately  following,  it  is  supposed  that  the  nucleus  of  the  sun 
would  give  a  continuous  spectrum  if  it  was  not  surrounded  by  gases 
and  metallic  vapors  that  absorb  some  of  the  rays  to  which  their  own 
spectra  correspond.  Just  as  the  D-line  corresponds  to  sodium,  so  the 
greater  number  of  the  Fraunhofer  lines  have  been  identified  in  the 
spectra  of  known  terrestrial  substances.  The  presence  of  at  least 
thirty-six  elements  in  the  sun's  atmosphere  has  been  thus  established, 
the  identity  of  the  absent  wave-frequencies  indicating  the  identity  of 
the  absorbing  media. 

(6)  The  indices  of  refraction  given  in  §  284  (c)  are  for  light  that 
has  the  particular  wave-frequency  that  corresponds  to  the  Fraunhofer 
D-line. 

308.  Laws  of  Spectra.  —  The  following  laws  have  been 
established  :  — 

(1)  Incandescent  solids  and  liquids  give  continuous 
spectra.  This  is  true  of  vapors  and  gases  also  when  they 


384  SCHOOL  PHYSICS. 

are  under  great  pressures.  The  spectrum  from  the  flame 
of  a  candle,  of  kerosene,  or  of  illuminating  gas  is  con- 
tinuous, being  due  to  the  incandescent  carbon  particles 
suspended  in  the  flame. 

(2)  Incandescent  rarefied  vapors  and  gases  give  discon- 
tinuous spectra  consisting  of  colored  bright  lines  or  bands. 
These  lines  or  bands  have  a  definite  position  for  each  sub- 
stance and  are,  therefore,  characteristic  of  it.     Thus  the 
sodium  spectrum  consists  of  bright  yellow  lines,  corre- 
sponding in  position  to  the  D-line  as  shown  in  Fig.  286. 

(3)  If  light  from  an  incandescent  solid  or  liquid  passes 
through  a  gas  at  a  temperature  lower  than  that  of  the  incan- 
descent body,  the  gas  absorbs  rays  of  the  same  degree  of 
refrangibility  as  that  of  the  rays  that  constitute  its  own 
spectrum.     This  absorption  is  somewhat  analogous  to  that 
mentioned  in  §  204.     The  result  is  a  spectrum  continuous 
except  as  interrupted  by  dark  lines  that  occupy  the  po- 
sition that  the  bright  lines  in  the  spectrum  of   the  gas 
itself  would   occupy.      Thus,  the  emission   spectrum   of 
sodium  corresponds  in  position  to  the  D-line  ;  the  sodium 
flame  absorbs  light   of  the   same   refrangibility,  and  its 
absorption  spectrum  falls  in  the  same  position. 

(a)  If  the  source  of  radiant  energy  under  spectroscopic  examina- 
tion is  approaching  the  observer,  the  effect  of  the  motion  will  be  the 
same  as  if  the  wave-length  was  shortened ;  the  characteristic  lines  will 
be  moved  toward  the  violet  end  of  the  spectrum.  If  the  source  of 
radiation  is  moving  from  the  observer,  the  opposite  effects  will  follow. 
Compare  §  192  (6).  Such  displacement  of  spectra  lines  has  enabled 
investigations  of  the  motions  of  even  the  "  fixed  "  stars. 

Experiment  267.  —  Hold  a  pane  of  glass  between  the  face  and  a 
hot  stove;  the  glass  shields  the  face  from  the  heat  of  the  stove. 
Hold  the  glass  between  the  face  and  the  sun ;  the  glass  does  not 
shield  the  face  from  the  heat  of  the  sun. 


SPECTRA,    CHROMATICS,    ETC.  385 

309.  Thermal  Effects  may  be  detected  throughout  the 
length  of  the  visible  spectrum  and  beyond  in  each  direc- 
tion, i.e.,  in  the  infra-red  spectrum  and  in  the  ultra-violet 
spectrum.     The  infra-red  radiation  is  of  longer,  and  the 
ultra-violet  radiation  is  of  shorter  wave-length  than  that 
of    any  part   of    the    visible   spectrum.      The   former  is 
present  in  the  spectrum  from  any  hot  body ;  the  latter, 
in  that  from  a  body  at  a  high  temperature,  as  the  incan- 
descent carbons  of  an  arc  electric  light.     When  radiant 
energy  is  considered  with  reference  to  its  heating  effects, 
it  is  sometimes  called  "radiant  heat,"  a  term  that  is  evi- 
dently misleading,  but  that  has  acquired  a  good  foot-hold 
in  the  literature  of  science.     Similarly,  the  radiation  of 
the  infra-red  region  is  spoken  of  as  "obscure  heat." 

(a)  Lenses  and  prisms  of  rock-salt  are  generally"  used  in  the  study 
of  the  heating  effects  of  radiant  energy,  as  glass  absorbs  much  of  the 
energy  of  the  longer  ether  waves,  as  was  shown  in  Experiment  267. 
When  a  solar  spectrum  is  produced  with  a  rock-salt  prism,  the  maxi- 
mum heating  effect  is  found  in  the  infra-red  region,  but  with  a  normal 
spectrum  (diffraction-spectrum,  §  315),  the  maximum  heating  effect 
coincides  somewhat  closely  with  the  maximum  luminous  effect. 

(6)  When  the  heating  effects  of  radiant  energy  rather  than  the 
luminous  effects  are  under  consideration,  the  ability  freely  to  trans- 
mit the  ether  waves  constitutes  diathermancy ;  the  corresponding 
inability  constitutes  athermancy.  In  other  words,  diathermanous 
corresponds  to  transparent,  and  athermanous  to  opaque.  Glass,  water 
and  alum  transmit  light,  but  absorb  nearly  all  of  the  energy  radiated 
from  a  vessel  filled  with  boiling  water,  i.e.,  they  are  transparent  and 
athermanous.  A  solution  of  iodine  in  carbon  disulphide  is  opaque 
and  diathermanous.  Dry  air  is  very  diathermanous ;  watery  vapor  is 
decidedly  athermanous. 

310.  Theory  of   Exchanges.  —  All   bodies   at  tempera- 
tures above  absolute  zero  must  radiate  energy  that  may 
be  converted  into  heat.     When  two  bodies  at  different 

25 


386  SCHOOL  PHYSICS. 

temperatures  are  placed  near  each  other,  one  gains  and 
the  other  loses  heat  by  radiation  until  both  ha^e  the  same 
temperature.  Each  radiates  to  the  other,  but  while  the 
inequality  of  temperature  continues,  the  hotter  body  gives 
more  than  it  receives,  and  vice  versa.  This  is  a  brief 
statement  of  Prevostfs  theory  of  exchanges. 

Absorption,  etc. 

Experiment  268.  —  When  there  is  snow  on  the  ground,  and  the 
sun  is  shining,  spread  a  piece  of  white  cloth  and  a  similar  piece  of 
black  cloth  on  the  snow,  and  notice  whether  the  snow  melts  more 
rapidly  under  one  than  under  the  other. 

Experiment  269.  —  Focus  a  sunbeam  on  the  clear  glass  bulb  of  an 
air  thermometer,  and  notice  the  feeble  effect  produced.  Coat  the  bulb 
with  candle  soot,  and  repeat  the  experiment.  Notice  the  greatly  in- 
creased effect. 

Experiment  270.  —  Secure  two  similar  pieces  of  tin-plate  at  least 
10  cm.  square.  Coat  one  face  of  one  of  the  pieces  with  lampblack 
(candle-soot).  Support  the  two  plates,  with  the  painted  surface  ver- 
tical, facing  the  other  plate,  and  about  10  cm.  from  it.  With  small 
bits  of  shoemaker's  wax,  fasten  a  small  ball  to  the  middle  of  the 
outer  face  of  each  plate.  Hold  a  hot  bod}T,  as  a  "  soldering  iron," 
midway  between  the  plates.  Xotice  which  ball  first  falls.  Repeat 
the  experiment  several  times  to  make  certain  whether  the  effect 
was  accidental  or  due  to  the  lampblack. 

Experiment  271.  —  Provide  two  bright  tin  cans  of  the  same  size 
and  shape.  In  the  cover  of  each,  make  a  hole  and  insert  the  bulb 
of  a  chemical  thermometer.  Blacken  the  outside  of  one  can  with 
lampblack.  Fill  both  cans  with  hot  water  from  the  same  vessel  and, 
consequently,  of  the  same  temperature.  At  the  end  of  half  an  hour, 
pass  the  bulb  of  the  thermometer  through  the  holes  in  the  covers, 
and  ascertain  the  temperature  of  the  water  in  each  can.  It  will  be 
found  that  the  blackened  can  has  radiated  its  heat  more  rapidly 
than  the  other.  Fill  both  cans  with  cold  water,  and  set  them  in  front 
of  a  hot  fire  or  in  the  sunshine.  The  temperature  of  the  water  in 


SPECTRA,    CHROMATICS,   ETC. 


387 


the  blackened  can  rises  more  rapidly  than  that  of  the  water  in  the 
other  can. 

4£ 

Experiment  272.  —  Secure  a  piece  of  stoneware  (Fig.  287)  of  any 
black  and  white  pattern.     Xotice  carefully  what  parts  absorb  the 
most  radiant  energy.      Heat 
the  plate  intensely,  view  it  in 


FIG.  287. 

a  darkened  room,  and  notice 
carefully  what  parts  radiate 
the  most  energy  (Fig.  288). 


FIG.  288. 


311.  Radiation,    Reflection    and    Absorption. -- Bodies 
differ  greatly  in  absorbing  power.     From  the  nature  of  the 
case,  a  good  absorber  is  a  poor  reflector.     Lampblack  is  a 
substance  of  maximum  absorbing  and  of  minimum  reflect- 
ing power.     Further  than  this,  the  emission  and  the  ab- 
sorption of  radiant  energy  go  hand  in  hand,  good  absorbers 
being   good   radiators,    and   good   reflectors   being    poor 
radiators,  and  vice  versa. 

312.  Chemical  Effects  may  be  detected  throughout  the 
length  of  the  visible  spectrum  and  beyond  in  each  direc- 
tion.    The  chemical  changes  upon  which  ordinary  pho- 
tography depends  are  most  stimulated  by  the  violet  and 
ultra-violet  rays  ;  this,  however,  is  not  true  of  all  chemical 
changes,  and  even  infra-red  photography  has  been  accom- 


388  SCHOOL  PHYSICS. 

plished.  By  exciting  molecular  agitation  of  the  molecules 
of  sulphide  of  zinc  with  an  electric  current  of  about 
10,000  alternations  per  second,  Nikola  Tesla  demon- 
strated, in  1894,  the  actinic  value  of  ucold  rays"  by 
taking  photographs  by  phosphorescent  light. 

(a)  It,  therefore,  appears  that  the  long-time  division  of  the  spec- 
trum into  three  parts,  heat,  light  and  actinism,  was  ill  founded ;  that 
from  one  end  of  the  spectrum  to  the  other,  the  radiation  differs  intrin- 
sically in  wave-length  only;  and  that  the  observed  diversity  of  effect 
is  due  to  the  character  of  the  surface  upon  which  the  radiation  falls. 

(b)  Lenses  and  prisms  of  quartz  are  generally  used  in  the  study  of 
the  chemical  effects  of  radiant  energy  as  they  absorb  less  of  the 
energy  of  the  short  ether  waves  than  do  those  of  glass. 

313.  Change  of  Vibration-Frequency.  —  When  solutions 
of  certain  substances,  such  as  esculin  and  sulphate  of 
quinine,  are  exposed  to  ultra-violet  radiation,  the  solu- 
tions lower  the  rate  of  vibration  to  that  of  an  opalescent 
blue  light.  This  property  of  lowering  the  vibration- 
frequency  of  ultra-violet  radiation  to  the  range  of  vision 
is  called  fluorescence.  Another  class  of  substances,  such 
as  the  sulphides  of  barium,  calcium,  and  strontium,  are 
luminous  when  carried  from  sunlight  into  a  dark  room 
and,  for  a  long  time  after,  present  the  general  appear- 
ance of  a  hot  body  cooling.  This  property  of  shining  in 
the  dark  after  exposure  to  light  is  called  phosphorescence. 
What  is  correctly  termed  phosphorescence  has  nothing  to 
do  with  phosphorus,  the  luminosity  of  which  in  the  dark 
is  due  to  slow  oxidation.  The  radiations  that  excite  this 
luminosity  are  those  of  high  wave-frequency,  so  that  phos- 
phorescence is  a  species  of  fluorescence  that  lasts  longer 
after  the  excitation  has  ceased  than  the  species  just 
described.  The  property  has  been  taken  advantage  of  for 


SPECTRA,    CHROMATICS,   ETC.  389 

the  production  of  what  are  called  "luminous  paints." 
The  luminous  rays  of  an  electric  arc  may  be  absorbed  by 
a  solution  of  iodine  in  carbon  disulphide,  and  the  residual 
infra-red  rays  reflected  or  refracted  to  a  focus.  A  piece 
of  platinum  or  of  charcoal  at  such  a  focus  of  non-luminous 
radiation  may  be  heated  to  incandescence.  This  raising 
of  the  vibration-frequency  of  infra-red  radiation  to  the 
range  of  vision  is  called  calorescence. 

CLASSROOM    EXERCISES. 

1.  Why  is  the  rainbow  a  circular  arc  instead  of    a  straight 
band? 

2.  What  does  a  wave-length  of  red  light  measure  in  centimeters  ? 

3.  Taking  the  velocity  of  light  to  be  186,000  miles  per  second 
and  the  wave-length  of  green  light  to  be  0.00002  of  an  inch,  how 
many  waves  per  second  beat  upon  the  retina  of  an  eye  exposed  to 
green  light  ? 

4.  How  may  spherical  and  chromatic  aberration  caused  by  a  lens 
be  corrected?  . 

5.  What  name  is  given  to  the  differential  deviation  by  refraction 
of  rays  of  different  wave-frequencies? 

6.  Why  is  a  rainbow  never  seen  at  noon  ? 

7.  Describe  Fraunhofer's  lines,  and  tell  how  they  may  be  pro- 
duced. 

8.  Under  what  circumstances  will  a  spectrum  be  (a)  continuous, 
( &)  bright-line  ;  (c)  dark-line  ? 

9.  Why  do  not  the  sun's  rays  heat  the  upper  atmosphere  of  the 
earth  as  they  pass  through  it  ? 

10.  Show  that  the  glass  walls  and  roof  of  a  greenhouse  are  a  trap 
for  solar  heat. 

11.  Why  is  it  oppressively  warm  when  the  sun  shines  after  a  sum- 
mer shower  ? 

12.  Why  is  there  greater  probability  of  frost  on  a  clear  than  on  a 
cloudy  night  ? 

13.  Explain  the  fact  that  the  glass  of  a  window  may  remain  cold 
while  the  sun's  radiations  are  pouring  through  it  and  heating  objects 
in  the  room. 


390 


SCHOOL  PHYSICS. 


14.  What  is  meant  by  the  statement  that  water  is  transparent  and 
athermanous  ? 

15.  What  is  meant  by  "radiant  heat,"  and  what  by  "obscure 
heat"?    Why  are  these  terms  objectionable? 

16.  How  can  you  cut  out  the  short-wave  radiations  of  an  arc  elec- 
tric lamp?     How  can  you  cut  out  the  long-wave  radiations? 

17.  Why  does  a  polished  tea-urn  remain  warm  longer  than  a  similar 
one  with  a  roughened  surface  ? 

18.  Explain  the  apparent  unsteadiness  of  an   object  seen  across 
the  top  of  a  hot  stove. 

19.  Show  that  the  watery  vapor  in  the  atmosphere  acts  as  a  blanket 
for  terrestrial  objects. 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Porte-lumiere  or  optical  lantern ;  crown- 
glass,  flint-glass,  and  carbon  disulphide  prisms ;  a  wooden  block, 
grooved  and  painted  black  ;  cyan-blue  and  orange  colored  glass;  pic- 
ric acid ;  copper  sulphate ;  ammonia  water ;  fine  platinum  wire ;  in- 
duction tube ;  voltaic  cell ;  Pliicker-tube ;  two  Leslie  cubes ;  pane  of 
window  glass  about  9  x  12  inches;  lampblack;  India-ink;  tin-foil; 
white-lead;  chemical  tank;  alum;  iodine;  carbon  disulphide. 

lw»  Cut  a  very  narrow  slit  with  straight,  smooth  edges  in  a  piece  of 
cardboard.  Fasten  the  cardboard  across  the  opening  of  a  porte- 
lumiere  or  an  optical  lantern,  with  the  slit  vertical.  With  a  convex 
lens  that  has  a  focal  distance  of  about  30  cm.,  project  an  image  of  the 
slit  upon  a  white  screen  at  a  considerable  distance.  Place  a  prism 

(60°)  of  crown-glass  between  the  lens 
and  screen,  close  to  the  lens  and  with 
its  edges  vertical.  Turn  the  prism 
about  its  axis  until  it  is  in  the  po- 
sition of  least  deviation.  Without 
changing  its  distance  from  the  lens, 
set  the  screen  so  that  the  light  re- 
fracted by  the  prism  falls  perpendicu- 
larly upon  it.  Describe  the  image  and 
mark  on  the  screen  its  limits,  and  the 
FIG.  289.  position  of  any  characteristic  points. 

Replace  the  crown-glass  prism  succes- 
sively with  flint-glass  and  carbon  disulphide  prisms,  and  note  any 
changes  in  the  spectrum.  Set  a  second  prism  near  the  first  and  with 


SPECTEA,    CHROMATICS,   ETC.  391 

its  base  turned  the  same  way,  as  shown  in  Fig.  289,  so  that  the  disper- 
sion effect  of  the  second  may  be  added  to  that  of  the  first,  and  note 
any  changes  in  the  spectrum. 

2.  Shorten  the  slit  used  in  Exercise  1  and  hold  the  second  prism 
with  its  edges  perpendicular  to  the  edges  of  the  first,  so  that  the  differ- 
ently colored  light  emergent  from  the  first  shall  be  received  upon  a 
face  of  the  second,  each  color  by  itself.     See  if  these  rays  of  differing 
wave-lengths  are  refracted  equally  by  the  second  prism. 

3.  Arrange  apparatus  as  described  in  Exercise  1,  and  cut  a  narrow 
vertical  slit  from  the  screen  so  that  light  of  some  one  color  may  pass 
through  the  slit.     Receive  this  light  upon  a  prism  behind  the  screen, 
and  see  if  there  is  any  further  dispersion,  or  any  production  of  new 
colors.     Explain  the  result  of  your  experiment. 

4.  Cut  a  slit  2.5  cm.  long  and  2  mm.  wide  in  each  of  two  pieces  of 
black  cardboard,  and  support  the  two  cards  in  a  groove  cut  in  a 
blackened  piece  of  wood.     The  width  of  the  groove  should  be  just 
twice  the  thickness  of  the  cards,  so  that  the  distance  between  the  slits 
may  be  adjusted  by  moving  the  cards  in  the  groove.      Repeat  Experi- 
ment 245,  and  hold  the  perforated  cardboard  screen  between  the  lens 
and  the  prism,  and  adjust  the  slits  so  that  light  of  only  two  colors  falls 
upon  the  lens.     Note  the  color  of  the  spot  formed  by  the  synthesis 
of  these  colors.     Try  other  pairs  of  colors,  and  note  the  resultant  color 
in  each  case.     Especially,  try  to  find  as  many  combinations  as  possible 
that  yield  white  light. 

5.  Place  the  three  disks  represented  in  Fig.  278  upon  the  whirling 
table,  and  fasten  them  in  position..     Turn  the  spindle  rapidly,  and  note 
the  color  of  the  blending.     Change  the  proportions  of  the  exposed 
colors,  and  blend  them  again.     Continue  the  work  with  a  view  of 
determining  the  accuracy  of  the  statement  that  any  color  of  the  spec- 
trum may  be  produced  by  the  composition  of  these  three  colors. 

6.  With  a  variety  of  similar  disks,  demonstrate  the  effect  of  blend- 
ing complementary  colors. 

7.  Admit  two  sunbeams  to  a  darkened  room,  and  cause  them  to 
overlap  on  a  white  screen.     Hold  a  piece  of  blue  glass  so  that  one  of 
the  beams  passes  through  it.     Pass  the  other  beam  through  a  piece 
of  glass  so  chosen  that  the  blending  of  the  two  colored  beams  pro- 
duces a  white  spot  on  the  screen.     Shut  off  one  of  the  beams,  and 
determine  the  effect  of  sending  the  other  through  both  of  the  pieces 
of  glass. 

8.  While  observing  the  solar  spectrum  with  a  spectroscope,  hold  a 


392  SCHOOL  PHYSICS. 

piece  of  cyan-blue  glass  over  the  slit  of  the  instrument,  and  note  the 
effect.  Then  try  a  piece  of  orange-colored  glass.  Then  study  the 
effect  when  the  two  pieces  are  superposed  in  front  of  the  slit.  Suc- 
cessively try  test-tube  portions  of  a  solution  of  picric  acid,  and  of  an 
ammoniacal  solution  of  copper  sulphate. 

9.  Make  a  loop  about  2  mm.  in  diameter  at  the  end  of  a  fine 
platinum  wire.  Fuse  a  small  bit  of  common  salt  into  this  loop. 
Place  an  alcohol  flame  just  beyond  the  slit  of  a  spectroscope.  Hold 
the  bead  of  salt  in  the  edge  of  the  flame  nearest  the  spectroscope  and  a 
little  below  the  level  of  the  slit.  Examine  the  spectrum,  and  map  the 
position  of  any  bright  lines  that  you  observe.  Devise  some  way  of 
producing  dark  lines  that  occupy  the  same  positions  in  the  spec- 
trum. 

10.  With  an  induction  coil,  illuminate  a  Pliicker-tube  containing 
some  known  gas,  and  examine  its  spectrum  with   a  spectroscope. 
Record  a  description  of  the  spectrum.     (See  §  506.) 

11.  Make  a  cubical  metal  vessel  with  edges  of  about  7  or  8  cm., 
and  vertical  faces  made  respectively  of  polished  brass,  sheet  lead, 
bright  tin-plate,  and  tin-plate  that  has  been  coated  with  lampblack. 
Leave  a  small  opening  in  the  upper  face.     Such  a  vessel  is  called  a 
Leslie  cube.     Fill  it  with  water,  and  bring  the  temperature  to  10°. 
Place  the  cube  3  or  4  cm.  from  an  air  thermometer  or  from  one  bulb 
of  a  differential  thermometer,  and  note  the  effect  upon  the  thermom- 
eter.    Raise  the  temperature  successively  to  20°,  30°,  40°,  etc. ;  bring, 
it  .within  the  same  distance  of  the  thermometer,  and  note  the  effect 
in  each  case.     Record  a  comparison  of  the  readings  of  the  mercury 
thermometer  in  the  cube  with  the  indications  of  the  air  thermometer, 
and  a  clear  statement  of  the  relation  between  them. 

12.  Repeat  one  of  the  tests  of  Exercise  11,  and  then  interpose  a  pane 
of  window  glass  between  the  cube  and  the  thermometer.     Explain  the 
effect  produced  by  the  screen. 

13.  With  the  same  apparatus,  test  the  absorptive  powers  of  tin-foil, 
lampblack,  India-ink,  and  white-lead  by  successively  coating  the  bulb 
of  the  air  thermometer  with  such  substances. 

14.  Test  the  radiating  powers  of  tin,  lampblack,  India-ink,  and 
white-lead  by  successively  turning  faces  of  the  Leslie  cube  thus  coated 
toward  the  bulb  of  the  air  thermometer,  being  careful  that  the  tem- 
perature and  the  distance  of  the  cube  are  the  same  in  each  instance. 
Try  to  find  some  relation  between  the  absorbing  powers  and  the  radi- 
ating powers  of  these  several   substances.      Also   similarly  test  the 


INTERFEKENCE,   DIFFRACTION,   POLARIZATION.       393 

radiating  powers  of  faces  of  the  cube  that  have  been  coated  with 
unglazed  white  paper  and  with  white  cotton  cloth. 

15.  Repeat  Experiment  228,  holding  a  "  chemical  tank  "  (see  Ex- 
periment 258)  so  that  the  sun's  rays  shall  pass  through  the  two  circu- 
lar windows  before  they  fall  upon  the  lens.  Fill  the  tank  with  a 
solution  of  alum  in  water,  and  repeat  the  experiment.  Determine  the 
effect,  if  any,  that  the  presence  of  the  tank,  empty  or  filled,  has  upon 
the  result  at  the  focus.  Empty  out  the  alum-water  and  fill  the  tank 
with  a  solution  of  iodine  in  carbon  disulphide,  and  repeat  the  experi- 
ment. 


VI.  INTERFERENCE,  DIFFRACTION,  POLARIZATION, 

ETC. 

Experiment  273.  —  In  any  convenient  clamp,  firmly  press  together 
the  centers  of  two  pieces  of  clean,  thick,  plate-glass.  Look  obliquely 
at  the  glass,  and  a  beautiful  play  of  colors  will  be  seen  surrounding 
the  point  of  greatest  pressure.  If  the  glass  is  illuminated  by  the 
monochromatic  light  of  a  sodium  flame  (see  Experiment  253),  yellow 
bands  separated  by  dark  bands  will  be  seen. 

314.  Interference  of  Light.  —  We  have  seen  that  two 
wave-motions  may  combine  in  such  a  way  as  to  neutralize 
each  other  (§  206),  and  that  such  an  interference  is  a 
peculiarity  of  wave  -motion,.  The  fact  that  light  may  thus 
neutralize  light  is  strong  confirmation  of  the  wave-theory. 

(a)  In  the  historical  experiment  of  which  Experiment  273  is  a 
modification,  a  plano-convex  lens  of  little  curvature  was  pressed  upon 
a  flat  piece  of  glass.  When  looked  at 

from  above,  the  center  of  the   lens  thus          -  I  ' 

used  is  surrounded  by  rainbow-like  bands     t^""""" — • —     f(     — — """"' 
of  color,  known  as  Newton  rings.     Of  the 
light  that  falls  vertically  upon   the  lens,  FIG.  290. 

some  is  reflected  at  the  curved  surface,  and 

some  from  the  upper  surface  of  the  plate  under  the  lens.  These 
latter  rays  have  to  traverse  twice  the  wedge-shaped  film  of  air  be- 
tween the  lens  and  the  plate.  Whenever  the  thickness  of  the  air- 
film  is  such  that  the  two  sets  of  reflected  waves  unite  in  opposite 


394 


SCHOOL  PHYSICS. 


phases,  interference  is  the  result.  If  the  apparatus  is  observed  by 
white  light,  and  the  red  rays  are  destroyed  at  a  certain  distance  from 
the  center  of  the  lens,  the  color  perceived  at  that  distance  will  be 
complementary  to  the  destroyed  red,  and  will  form  a  circular  green 
band.  If  the  apparatus  is  observed  by  red  light,  a  dark  ring  will  ap- 
pear at  the  same  distance.  At  another  distance  from  the  center  of 
the  lens,  the  violet  rays  will  be  destroyed,  and  the  circular  band  seen 
at  that  distance  will  be  due  to  the  combination  of  the  other  constit- 
uent rays  of  the  light  used. 

(&)  Interference  colors  similarly  produced  by  reflection  are  often 
seen  in  soap  bubbles,  in  small  quantities  of  oil  that  have  been  spread 
over  large  sheets  of  water,  in  mica,  selenite,  ice,  and  other  crystals. 
Certain  striated  surfaces,  like  those  of  mother-of-pearl,  some  kinds  of 
shells  and  feathers,  etc.,  owe  their  beautiful  colors  to  the  interference 
of  reflected  light  (see  §  315,  6). 

Diffraction. 

Experiment  274.  —  With  a  fine  needle,  rule  a  number  of  fine  parallel 
lines  upon  a  piece  of  glass  that  has  been  coated  with  India-ink.  Take 
pains  to  cut  through  the  ink  to  the  glass.  Cut  a  slit  2  mm.  wide  in  a 
black  card,  and  hold  it  at  arm's  length  in  front  of  a  flame.  Hold  the 
glass  close  to  the  eye  and,  through  the  scratched  lines,  look  at  the  slit. 
Notice  the  series  of  spectra  on  each  side  of  the  slit. 

Experiment  275.  —  Throw  a  sunbeam  through  a  very  small  opening 
in  the  shutter  of  a  darkened  room.  Receive  the  beam  upon  a  convex 


FIG.  291. 

lens  of  short  focal  length,  placing  a  piece  of  red  glass  between  the 
aperture  and  the  lens.  Place  an  opaque  screen  with  a  sharp  edge 
beyond  the  focal  distance  of  the  lens,  as  at  a,  so  as  to  cut  off  the  lower 
part  of  the  cone  of  homogeneous  light,  and  project  the  upper  part 
thereof  upon  a  screen  at  b.  A  faint  light  is  seen  on  the  screen  below  the 
level  of  a  and,  therefore,  within  the  geometrical  shadow.  The  part  of  the 
screen  immediately  above  the  level  of  a  contains  a  series  of  dark  and 
light  bands,  as  shown  at  B,  which  is  a  front  view  of  the  screen  at  b. 


INTERFERENCE,    DIFFRACTION,    POLARIZATION.       395 

315.  Diffraction. — When  water  waves  strike  an  obstacle, 
part  of  the  energy  of  the  wave  is  expended  in  producing  a 
second  set  of  waves  that  seem  to  circle  outward  from  the 
side  of  the  obstacle  as  a  center.  The  original  wave 
(primary)  passes  directly  onward,  while  the  secondary 
waves  wind  around  behind  the  obstacle.  In  similar  man- 
ner, sound  bends  around  a  corner,  but  sound-shadows  may 
be  produced  if  the  wave-length  is  sufficiently  small,  or  if 
the  obstacle  is  of  great  size  compared  with  the  length  of 
the  sound  waves.  So  ether  waves  are  modified  when  they 
traverse  a  minute  opening  or  narrow  slit,  or  impinge  upon 
an  obstacle,  e.g.,  a  hair,  so  small  as  to  be  comparable 
with  the  wave-length.  The  phenomena  are  identical 
when  the  scale  of  the  ex- 
periment is  the  same. 
If  a  beam  of  monochro- 
matic light  is  passed 
through  a  narrow  slit 

and  received  upon  a  screen  in  a  dark  room,  a  series  of 
alternately  light  and  dark  bands  or  "  fringes "  is  seen  ; 
if  white  light  is  employed,  a  series  of  colored  spectra  is 
obtained.  Thus  it  appears  that,  under  proper  conditions, 
rays  may  be  bent  and  caused  to  penetrate  into  the  shadow. 
The  interference-phenomena  resulting  from  this  action  are 
called  diffraction. 

(a)  As  the  primary  and  secondary  waves  cut  each  other,  they 
unite  at  some  points,  crest  with  crest  and,  at  other  points,  crest 
with  trough.  At  the  latter  points,  we  have  interference  of  light 
and  the  effects  of  colors  produced  thereby  as  explained  above. 
The  halos  sometimes  seen  around  the  sun  and  moon  are  due  to 
the  diffraction  of  light  by  watery  globules  in  the  atmosphere.  The 
colors  often  seen  on  looking  through  a  feather  or  one's  half-closed 


396 


SCHOOL  PHYSICS. 


eyelashes   at   a  distant  source   of    brilliant    light   are   also  due  to 
diffraction. 

(&)  When  lines  are  ruled  on  the  surface  of  glass,  the  ruled  lines 
become  opaque,  the  spaces  between  them  remaining  transparent.  A 
system  of  close,  equidistant,  parallel  lines  ruled  on  glass,  or  on  polished 
(speculum)  metal,  constitutes  a  diffraction  grating.  Lines  are  ruled 
for  this  purpose  at  the  rate  of  10,000  to  20,000  or  even  40,000  to  the 
inch.  Such  gratings  yield  interference  or  diffraction  spectra,  which  are 
much  used  in  spectroscopic  work,  and  afford  a  simple  means  for 
measuring  the  wave-length  of  ether  vibrations.  In  these  spectra,  the 
colors  are  distributed  in  their  true  order  and  extent  according  to  their 
differences  in  wave-length;  while,  in  prismatic  spectra,  the  less  re- 
frangible (red)  rays  are  crowded  together,  and  the  more  refrangible 
B  C  D  E  F  O  H,. 


H,H., 


B  C          D  E  F  G 

FIG.  293. 

(violet  and  blue)  are  correspondingly  dispersed.  For  this  reason,  the 
diffraction  spectrum  is  called  a  normal  spectrum.  The  upper  part  of 
Fig.  293  represents  a  normal  spectrum,  and  the  lower  part,  a  prismatic 
spectrum.  Comparing  the  two,  the  "irrationality  of  dispersion"  of 
the  prismatic  spectrum  is  seen. 

316.    Irradiation  is  the  apparent  enlargement  of  a  strongly 

illuminated  object 
when  seen  against  a 
dark  ground.  Thus, 
when  the  two  equal 
circles  shown  in 
Fig.  294  are  care- 
fully observed  in  a 
FIG.  294.  J 

good    light,    one 

seems  to  be  larger  than  the  other. 


INTERFERENCE,   DIFFRACTION,   POLARIZATION.       397 


(a)  Irradiation  increases  with  the  brightness  of  the  object, 
diminishes  as  the  illumination  of  the  object  and  that  of  the  field  of 
view  approach  equality,  and  vanishes  when  they  become  equal.  This 
effect  is  very  perceptible  in  the  apparent  magnitude  of  stars,  which 
look  much  larger  than  they  otherwise  would ;  also  in  the  appearance 
of  the  new  moon,  the  illuminated  crescent  seeming  to  extend  beyond 
the  darker  portion,  as  if  the  new  moon  was  holding  the  old  moon  in 
its  arms. 

Polarization. 

Experiment  276.  —  While  looking  through  the  plates  of  a  pair  of 
tourmaline  tongs,  turn  one  of 
the  plates  in  its  wire  support. 
The  intensity  of  the  light 
transmitted  will  vary  as  the 
plate  is  turned.  When  little 
or  no  light  is  transmitted,  the  FIG.  295. 

plates  are  said  to  be  "  crossed." 

Experiment  277.  —  Write  your  name  on  a  sheet  of  paper,  and  cover 
it  with  a  crystal  of  Iceland  spar.  The  lines  will  appear  double,  as 

shown  in  Fig.  296.  Place 
the  crystal  over  a  dot  on  the 
paper,  hold  the  eye  directly 
over  the  dot,  and  slowly  turn 
the  crystal  around ;  one  of 
the  two  images  of  the  dot 
will  revolve  about  the  other 
image.  Prick  a  pin-hole 
through  a  card,  and  hold  the 
card  against  one  side  of  the 
crystal,  look  through  the  crystal  at  the  pin-hole,  and  rotate  the  crystal 
as  before. 

Experiment  278.  —  Look  through  one  of  the  plates  of  the  tourmaline 
tongs  (Fig.  295)  at  the  two  images  of  the  dot  formed  by  the  double 
refraction  of  the  Iceland  spar  as  described  in  Experiment  277.  One 
of  the  images  will  be  much  fainter  than  the  other.  Turn  the  tourma- 
line plate  slowly  around,  and  notice  that  one  image  grows  fainter  and 
the  other  brighter,  the  maximum  brightness  of  one  being  simultane- 
ous with  the  extinction  of  the  other. 


FIG.  296. 


398  SCHOOL  PHYSICS. 

317.  Polarization  of  Light.  —  Common  white  light  is  a 
highly  complex  form  of  radiant  energy,  comprising  not 
only  an  indefinite  number  of  wave-lengths,  but  also  an  in- 
definite number  of  modes  of  ether  vibration.  When  a 
rope  is  shaken  as  described  in  Experiment  110,  the  vibra- 
tions of  the  wave  thus  produced  will  lie  in  a  vertical  plane  ; 
when  the  hand  is  moved  horizontally,  the  vibrations  will 
lie  in  a  horizontal  plane.  It  thus  appears  that  a  transverse 
wave  is  capable  of  assuming  a  particular  side  or  direction  ; 
a  longitudinal  wave  is  not.  In  like  manner,  a  single  row 
of  ether  particles  engaged  in  propagating  a  linear  trans- 
verse wave  may  describe  any  one  of  a  variety  of  paths, 
each  perpendicular  to  the  line  of  propagation  of  the  radia- 
tion. For  example,  each  particle  may  vibrate  in  a  straight 
line,  parallel  to  the  wave-front  and  indiffer- 
ently in  any  plane  about  the  line  of  propa- 
gation, as  represented  in  Fig.  297.  If  all 
the  ether  particles  in  the  row  under  consid- 
eration successively  vibrate  along  lines  lying 
in  the  same  plane,  the  radiation  is  said  to  be  plane- 
polarized,  and  the  wave  thus  constituted  is  called  a 
plane-polarized  wave.  A  change  ~by  which  the  transverse 
vibrations  of  luminous  waves  are  limited  to  a  single  direc- 
tion is  called  polarization  of  light.  This  change  may  be 
produced  in  several  ways. 

(a)  Light  may  be  polarized :  — 

(1)  By  reflection  from  the  surface  of  glass,  water,  and  other  non- 
metallic  substances.      The  degree   of   polarization  reaches  its  maxi- 
mum when  the  angle  of  incidence  lias  a  certain  value  depending  upon 
the  substance,  and  called  the  angle  of  polarization.     For  glass,  this 
angle  is  54^°. 

(2)  By  transmission  through   a  series   of  transparent  plates  of 


INTERFERENCE,    DIFFRACTION,    POLARIZATION.       399 

glass  placed  in  parallel  position  at  the  proper  angle  to  the  inci- 
dent ray. 

(3)  By  double  refraction,  as  in  the  case  of  Iceland  spar  or  of  a  plate 
cut  in  a  certain  way  from  a  tourmaline  crystal.  A  beam  of  light, 
falling  upon  such  a  crystal,  is  generally  split  into  two  parts  polarized  at 
right  angles.  One  of  these  parts  obeys  the  regular  law  of  refraction, 
and  is  called  the  ordinary  ray ;  the  other  does  not,  and  is  called  the 
extraordinary  ray.  A  prism  of  Iceland  spar  prepared  in  such  a  way 
that  one  beam  of  polarized  light  is  totally  reflected  and  extinguished, 
w^hile  the  other  beam  passes  through  as  polarized  light,  is  called  a 
Nicol  prism.  Xicol  prisms  and  tourmaline  plates  are  largely  used  in 
experiments  with  polarized  light. 

(6)  Light  that  has  passed  through  a  tourmaline  plate  differs  so 
much  from  ordinary  light  that  it  may  be  stopped  by  a  similar  plate, 
as  was  seen  in  Experiment  276.  For  the  sake  of  simplicity,  imagine 
the  indifferently  placed  planes  of  vibration,  as  represented  in  Fig. 
297,  to  be  resolved  into  two  that  lie  at  right  angles  to  each  other,  as 
shown  in  Fig.  298.  Then  the  action 
of  the  first  tourmaline  plate  may  be 
compared  to  that  of  a  vertical-bar 
grating  that  allows  the  vibrations  in  a 
vertical  plane  to  pass,  but  absorbs  the 
vibrations  that  lie  in  a  horizontal  FIG.  298. 

plane.     Evidently,  the  vibrations  that 

pass  one  such  grating,  as  T,  will  pass  others  similarly  placed,  but 
will  be  stopped  by  one  that  is  crossed,  as  at  T' .  The  part  of  the 
beam  that  lies  between  T  and  ^represents  plane  polarized  light. 

(c)  Polarized  light  presents  to  the  unaided  eye  the  same  appear- 
ance as  common  light.  An  instrument  for  producing  and  testing 
polarized  light  is  called  a  polariscope.  It  consists  of  two  characteristic 
parts;  one,  used  to  produce  polarization  and  called  the  polarizer ;  the 
other,  used  to  test  or  to  study  the  polarized  light  and  called  the  analyzer. 
Apparatus  that  serves  for  either  of  these  purposes  will  serve  for  the 
other.  The  Xicol  prism  is  generally  preferred  for  both  purposes. 
Some  of  the  color-effects  due  to  the  interference  of  polarized  light  are 
very  beautiful. 

(rf)  The  plane  of  polarization  may  'be  rotated  by  passing  plane- 
polarized  light  through  certain  substances,  some  substances  producing 
a  right-hand  rotation  and  others  a  left-hand  rotation.  This  property 
of  polarized  light  has  been  applied  to  the  estimation  of  the  commercial 


400  SCHOOL  PHYSICS. 

value  of  sugar  by  the  amount  of  rotation  produced  by  a  solution  of  it 
of  known  strength.  The  devices  for  the  precise  measurement  of  the 
amount  of  rotation  involve  advanced  scientific  principles.  When 
plane  polarized  light  is  passed  through  a  plate  of  quartz  cut  perpen- 
dicularly to  the  axis,  the  plane  of  polarization  is  turned  through  an 
angle  that  varies  with  the  thickness  of  the  plate  and  the  wave-length 
of  the  light.  Thus,  if  a  pebble  spectacle-lens  is  placed  between 
crossed  tourmaline  plates,  the  dark  field  is  brightened,  and  generally 
colored,  by  the  transmitted  light. 

(e)  Light  may  be  circularly  and  elliptically  polarized  as  well  as 
plane  polarized. 

Note.  —  For  a  fuller  discussion  of  the  polarization  of  radiant 
energy,  the  pupil  is  referred  to  some  special  work  on  Light.  The 
subject  is  interesting  and  the  phenomena  are  beautiful. 


VII.    A  FEW  OPTICAL   INSTRUMENTS. 

Experiment  279.  —  Stick  two  needles  into  a  board  about  6  inches 
apart.  Close  one  eye,  and  hold  the  board  so  that  the  needles  shall  be 
nearly  in  range  with  the  open  eye  and  about  6  and  12  inches  respec- 
tively from  it.  One  needle  will  be  seen  distinctly  while  the  image  of 
the  other  will  be  blurred.  Fix  the  view  definitely  on  the  needle  that 
appears  blurred  and  it  will  become  distinct,  but  you  cannot  see  both 
clearly  at  the  same  time. 

Experiment  280.  —  Cover  half  of  a  white  sheet  of  paper  with  a 
sheet  of  black  paper.  Fix  the  eye  intently  on  the  middle  of  the  white 
surface  for  fifty  or  sixty  seconds.  Keep  the  eye  fixed  on  the  same 
point,  and  suddenly  remove  the  black  paper.  The  newly  exposed  part 
of  the  sheet  appears  more  brilliantly  illuminated  than  the  other. 

Experiment  281.  —  Stick  a  bright  red  wafer  upon  a  piece  of  white 
paper.  Hold  the  paper  in  a  bright  light  and  look  steadily  at  the 
wafer,  for  some  time,  with  one  eye.  Turn  the  eye  quickly  to  another 
part  of  the  paper  or  to  a  white  wall,  and  a  greenish  spot,  the  size  and 
shape  of  the  wafer,  will  appear.  The  greenish  color  of  the  image  is 
complementary  to  the  red  of  the  wafer.  If  the  wafer  is  green,  the 
image  afterwards  seen  will  be  of  a  reddish  (complementary)  color. 


A  FEW  OPTICAL  INSTRUMENTS.  401 

Experiment  282.  —  Close  one  eye  and  try  to  thread  a  needle.  Bend 
a  stout  wire  at  a  right  angle,  and  try  to  pass  one  end  of  it  through  a 
ring  held  at  arm's  length,  one  eye  being  closed. 

Experiment  283.  —  Prick  a  pin-hole  in  a  card,  hold  it  near  the  eye, 
and  look  through  the  pin-hole  at  a  pin  held  at  arm's  length.  As  the 
pin  is  slowly  moved  toward  the  eye,  the  visual  angle  (§  318,  e)  increases 
and  the  pin  seems  to  grow  larger. 

318.  The  Human  Eye,  optically  considered,  is  an  ar- 
rangement for  projecting  inverted,  real  images  upon  a 
screen  made  of  nerve  filaments.  This  image  is  the  origin 
of  the  sensation  of  vision.  The  luminous  waves  transfer 
their  energy  to  the  nerve  filaments,  they  transmit  it  to 
the  brain  and,  in  some  mysterious  way,  the  sensation 
follows. 

(a)  The  most  essential  parts  of  this  instrument  are  contained  in 
the  eyeball,  a  nearly  spherical  body,  about  an  inch  in  diameter,  and 
capable  of  being  turned  considerably  in  its  socket  by  the  action  of 
various  muscles.  It  is  represented  in  section  from  front  to  back 
by  Fig.  299.  The  greater  part  of  the  outer  coat  is  tough  and  opaque, 
and  is  called  the  "  white  of  the  eye  " 
or  the  sclerotic  coat,  S ;  the  front  part 
of  the  coat  is  a  hard,  transparent 
structure  called  the  cornea,  C.  The 
cornea  is  more  convex  than  the  rest 
of  the  eyeball,  and  fits  into  the  scle- 
rotic as  a  watch-crystal  does  into  its 
case.  The  chief  part  of  the  second 
tunic  of  the  eye  is  the  choroid  coat, 
N,  which  is  opaque  and  intensely 
black,  and  absorbs  all  internally  re-  FIG  299. 

fleeted   light.      The   third   or  inner 

tunic  is  the  retina,  R,  an  expansion  of  the  optic  nerve  which  enters 
the  eyeball  from  behind.  These  several  tunics  or  coats  form  a  kind 
of  camera  filled  with  solid  and  liquid  refractive  media.  The  crys- 
talline lens,  L,  a  solid  biconvex  body,  is  suspended  in  the  middle  of 
this  camera  and  directly  in  the  axis  of  vision.  Its  shape  is  shown 
26 


402  SCHOOL  PHYSICS. 

in  the  figure ;  it  tends  to  flatten  with  age.  With  its  capsule,  it  divides 
the  eye  into  two  compartments,  and  is  chiefly  instrumental  in  bring- 
ing the  rays  of  light  to  a  focus  on  the  retina.  The  larger  chamber 
of  the  eyeball  is  filled  with  a  transparent,  jelly-like  substance,  F,  that 
resembles  the  white  of  an  egg,  is  called  the  vitreous  humor,  and  is 
enclosed  in  the  delicate  hyaloid  membrane,  H.  The  chamber  between 
the  cornea  and  the  lens  is  filled  with  a  more  watery  liquid,  the  aqueous 
humor.  This  anterior  chamber  is  partly  divided  into  two  compart- 
ments by  an  annular  curtain,  /,  called  the  iris.  This  curtain  is 
opaque,  and  its  color  constitutes  the  color  of  the  eye.  The  circular 
opening  in  the  iris  is  called  the  pupil  The  iris  acts  as  a  self-regulat- 
ing diaphragm,  dilating  the  pupil  and  thus  admitting  more  light 
when  the  illumination  is  weak ;  contracting  the  pupil  and  cutting  off 
more  light  when  the  illumination  is  strong. 

(ft)  That  vision  may  be  distinct,  the  image  formed  on  the  retina 
must  be  clearly  defined,  well  illuminated,  and  of  sufficient  size.  With- 
out our  consciousness,  the  muscular  action  of  the  eye  changes  the 
curvature  of  the  crystalline  lens  so  that  rays  from  near  or  distant 
objects  may  be  focused  on  the  retina.  Instead  of  moving  the  screen, 
the  refractive  power  of  the  lens  is  changed.  This  power  of  "  accom- 
modation," or  automatic  adjustment  for  distance,  is  limited.  When  a 
book  is  held  close  to  the  eyes,  the  rays  from  the  letters  are  so  divergent 
that  the  eye  cannot  focus  them  upon  the  retina.  The  near  point  of 
vision  is  generally  about  3|  inches  from  the  eye.  As  parallel  rays  are 
generally  brought  to  a  focus  on  the  retina  when  the  eye  is  at  rest,  the 
far  point  for  good  eyes  is  infinitely  distant.  Owing  to  the  small  size 
of  the  pupil,  rays  from  a  point  20  inches  or  more  distant  are  practi- 
cally parallel.  The  near  point  of  some  eyes  is  less  than  3J-  inches, 
while  the  far  point  is  only  8  or  10  inches.  Such  eyes  are  myopic  and 
their  owners  are  near-sighted;  the  retina  is  too  far  back,  the  eyeball 
being  elongated  in  the  direction  of  its  axis.  The  remedy  is  in  concave 
glasses.  The  near  point  of  some  eyes  is  about  12  inches  and  the  far 
point  is  infinitely  distant.  Such  eyes  are  hypermetropic  and  their 
owners  are  far-sighted.  In  such  eyes  the  retina  is  too  far  forward,  the 
eyeball  being  flattened  in  the  direction  of  its  axis.  The  remedy  is  in 
convex  glasses.  When  the  diminished  power  of  accommodation  for 
near  objects  is  an  incident  of  advancing  years,  and  due  to  the  progres- 
sive loss  of  elasticity  in  the  crystalline  lens,  the  eyes  are  presbyopic 
and  their  owners  are  old-sighted.  The  cause  of  the  difficulty  is  different 
from  that  of  far-sightedness,  but  the  remedy  is  the  same. 


A  FEW  OPTICAL  INSTRUMENTS.  403 

(c)  The  impression  upon  the  retina  does  not  disappear  instantly 
when  the  action  of  the  light  ceases,  but  continues  for  about  an  eighth 
of  a  second.  The  result  is  what  is  called  the  persistence  of  vision.  If 
the  impressions  are  repeated  within  the  interval  of  the  persistence  of 
vision,  they  appear  continuous.  This  phenomenon  is  well  illustrated 
by  the  luminous  ring  produced  by  swinging  a  firebrand  around  a 
circle,  and  in  the  action  of  the  common  toy  known  as  the  thaumatrope 
or  the  zoetrope. 

(W)  The  retina  is  thickly  studded  with  microscopic  projections 
called  rods  and  cones,  the  terminal  elements  of  the  optic  nerve. 
According  to  a  theory  that  is  as  yet  purely  provisional,  these  end- 
organs  are  tuned  to  sympathetic  vibrations  with  the  ether  vibrations 
that  severall}T  correspond  to  violet,  green,  and  red  (§  299,  a),  and  by 
combining  these  effects  in  suitable  proportions,  the  several  color- 
sensations  are  produced.  When  any  of  these  end-organs  are  inopera- 
tive or  when  they  are  not  equally  sensitive,  the  person  is  affected 
with  color-blindness,  i.e.,  he  is  unable  to  recognize  certain  colors, 
generally  red.  Sometimes  these  terminal  elements  seem  to  become 
tired  of  vibrating  at  a  given  rate  and  thus  to  become  insensible  to  a 
certain  color.  (See  Experiments  280  and  281.)  Hence,  what  is  known 
a»  subjective  color  is  due  to  a  retinal  fatigue.  In  the  middle  of  the 
retina  and  in  the  axis  of  the  eye  is  a  little  rounded  elevation  called 
the  yellow  spot  or  macula  lutea.  It  is  the  most  sensitive  part  of  the 
retina.  On  the  nasal  side  of  the  yellow  spot  is  the  entrance  of 
the  optic  nerve  and  its  central  artery.  As  this  part  of  the  retina 
lacks  the  visual  function  that  characterizes  the  rest  of  its  surface,  it 
is  called  the  blind  spot. 

(c)  The  estimation  of  distances  by  the  eye  is  a  matter  of  judgment 
and  is  chiefly  based  upon  experience.  This  experience  relates  to  the 
amount  of  muscular  effort  exerted  in  adjusting  the  eye  for  distinct 
vision,  and  in  turning  the  two  eyes  inward  so  that  their  axes  meet  at 
the  object,  thus  forming  the  optical  angle  (see  Experiment  282)  ;  to  the 
comparison  of  the  angle  formed  by  lines  drawn  from  the  extremities 
of  the  object  to  either  eye  and  called  the  visual  angle  with  the  visual 
angle  subtended  by  objects  of  known  size  and  distance ;  and  to  the 
observation  of  changes  of  color  and  brightness  produced  by  the  varying 
thickness  of  the  air  through  which  the  object  is  viewed. 

(/")  The  estimation  of  the  size  of  distant  objects  is  also  a  matter 
of  judgment,  based  upon  the  known  or  supposed  distance  of  the  object. 
The  ratio  between  the  size  of  object  and  image  equals  the  ratio 


404 


SCHOOL  PHYSICS. 


between  the  distance  of  each  from  the  lens,  and  the  mind  uncon- 
sciously  bases  its  conclusions  on  this  fact. 

Stereoscopic  Effect. 

Experiment  284.  —  Close  the  left  eye,  and  hold  the  right  hand  so 
that  the  forefinger  hides  the  other  three  fingers.  Without  changing 
the  position  of  the  hand,  open  the  left  and  close  the  right  eye.  The 
hidden  fingers  become  visible  in  part.  It  is  evident  that  the  images 
upon  the  retinas  of  the  two  eyes  are  different. 

Experiment  285.  —  Place  a  die  on  the  table  directly  in  front  of  you. 
Looking  at  it  with  only  the  left  eye, 
three  faces  are  visible,  as  shown  at  A, 
Fig.  300.  Looking  at  it  with  only  the 
right  eye,  it  appears  as  shown  at  B.  If, 
in  any  way,  we  combine  two  such  draw- 
ings, so  as  to  produce  images  upon  the 
retinas  of  the  two  eyes  like  those  pro- 
duced by  the  solid  object,  we  obtain  the  idea  of  solidity. 


• 

A. 


r. 


B 


FIG.  300. 


319.  The  Stereoscope  is  an  instrument  for  illustrating 
the  phenomena  of  binocular  vision,  and  for  producing  from 
two  nearly  similar  pictures  of  an  object  the  effect  of  a 
single  picture  with  the  appearance  of  relief  and  solidity 
that  pertains  to  ordinary  vision. 

(a)  The  stereoscopic  view  or  slide  shows,  side  by  side,  two  pic< 
tures  taken  under  a  slightly  different  angular  view.  It  is  the  office 
of  the  stereoscope  to  blend 
these  two  pictures.  As  in 
ordinary  vision,  each  eye 
sees  only  one  of  the  pictures, 
but  the  two  images  conveyed 
to  the  brain  unite  into  one. 
The  diaphragm,  Z),  prevents 
either  eye  from  seeing  both 
pictures  at  the  same  time. 
Rays  of  light  from  B  are 
refracted  by  the  half-lens,  FIG.  301. 

E't  so  that  they  seem  to  come  from  C,  beyond  the   plane  of  the 


A  FEW  OPTICAL  INSTRUMENTS.  405 

pictures.  In  the  same  way,  rays  from  A  are  refracted  by  E  so  that 
they  also  seem  to  come  from  C.  The  two  slightly  different  pictures, 
thus  seeming  to  be  in  the  same  place  at  the  same  time,  are  success- 
fully blended ;  the  picture  "  stands  out,"  or  has  the  appearance  of 
solidity. 

320.  The  Photographer's  Camera  corresponds  to  the 
camera-obscura  described  in  §  265.  '  A  darkened  box, 
DE,  adjustable  in  length,  takes  the  place  of  the  darkened 
room,  and  an  achromatic  convex  lens  is  substituted  for 
the  aperture  in  the  shutter. 

(a)  A  ground-glass  plate  is  placed  in  the  frame  at  E,  which  is 
adjusted  so   that   a  well-defined   inverted   image   of   the   object   in 
front  of  A   is  projected   upon 
the   glass  plate   as    shown    in 
Fig.  302.     This  adjustment  is 
completed  by  moving  the  lens 
and   its   tube   by  the   toothed 
wheel  at  />.     When  the  focus- 
ing is  satisfactory,  A   is  cov- 
ered, the  ground-glass  plate  is 
replaced  by  a  chemically  pre- 
pared sensitive  plate,  A  is  un- 
covered,  and   the   image   pro- 
jected  on    the   chemical  film.    -  FIG.  302. 
The  chemical  changes  that  the 

light  produces  in  the  film  are  made  visible  by  a  process  called 
"developing,"  and  made  permanent  by  a  process  called  "fixing." 

Microscope. 

Experiment  286.  —  Provide  two  small  biconvex  lenses  about  4  cm. 
in  diameter,  one  with  a  focal  length  of  about  3  cm.  and  the  other 
with  a  focal  length  of  about  5  cm.  Mount  each  by  inserting  its 
edge  in  a  slit  in  a  large  cork.  Place  a  small  bright  object  in 
front  of  the  lens  of  shorter  focal  length  and  close  to  it,  and  adjust 
a  screen  on  the  other  side  of  the  lens  so  that  a  sharp  image  of 
the  object  will  be  projected  on  it.  Place  the  other  lens  back  of  the 
screen,  and  at  a  distance  from  it  less  than  the  focal  length  of  the 


406 


SCHOOL  PHYSICS. 


lens.  Remove  the  screen,  and  look  through  the  second  lens  toward 
the  first.  Adjust  the  second  lens  until  you  can  see  a  virtual  image 
of  the  real  image  of  the  object. 

321.  A  Microscope  consists  of  a  lens  or  a  combination  of 
lenses  used  to  observe  small  objects,  often  so  minute  as 
to  be  invisible  to  the  unaided  eye. 

(a)  The  simple  microscope  is  generally  a  single  convex  lens,  and 
is  often  called  a  magnifying  glass.      The  object  is  placed  between 
the  lens  and  its  principal  focus.     The  lens  increases  the  visual  angle. 
The  image  is  virtual,  erect,  and  magnified. 

(b)  The  magnifying  power  of  a  lens  is  the  ratio  between  the  length 
of  the  object  and  the  length  of  its  image. 

(c)  The  compound  microscope  consists  essentially  of  two  lenses  or 

systems  of  lenses.  One  of  these,  0, 
called  the  objective,  is  of  short  focus. 
The  object,  AB,  being  placed  slightly 
beyond  the  principal  focus,  a  real  image, 
cd,  magnified  and  inverted  is  formed. 
The  other  lens,  E,  called  the  eyepiece 
or  ocular,  is  so  placed  that  the  image, 
cd,  lies  between  it  and  its  focus.  A 
magnified,  virtual  image  of  the  real 
image,  cd,  is  formed  by  the  eyepiece 
and  seen  by  the  observer  at  ab.  Eye- 
piece and  objective  are  placed  at  op- 
posite ends  of  a  tube  and  are  generally 
compound,  the  objective  consisting  of 
two  or  three  achromatic  lenses,  and  the 
eyepiece  of  two  or  more  simple  lenses. 
The  instrument  varies  widely  in  con- 
struction, and  is  often  provided  with 
many  accessories  or  special  devices  ap- 
plicable to  particular  uses. 

Experiment  287.  —  Using  a  biconvex 
lens  about  10  cm.  in  diameter  and 
with  a  focal  length  of  about  40  cm.,  project  a  sharp  image  of  a 
distant  object  on  a  screen.  Back  of  the  screen,  place  the  lens  of 


A  ^FEW  OPTICAL   INSTRUMENTS.  407 

3  cm.  focal  length  that  was  used  in  Experiment  286.  The  distance 
of  the  lens  from  the  screen  should  be  less  than  the  focal  length  of 
the  lens.  Remove  the  screen,  and  look  through  the  second  lens 
toward  the  first.  Adjust  the  second  lens  until  you  can  see  a  virtual 
image  of  the  real  image  of  the  object. 

322.  A  Telescope  is  an  instrument  designed  for  the  obser- 
vation of  distant  objects,  and  consists  essentially  of  an 
objective  for  the  formation  of  an  image  of  the  object 
and  of  an  eyepiece  for  magnifying  this  image.  The 
optical  parts  are  generally  set  in  a  tube  so  arranged  that 
the  distance  between  the  objective  and  the  eyepiece  may 
be  adjusted  for  distinct  vision.  A  telescope  is  refracting 
or  reflecting  according  as  its  objective  is  a  convex  lens  or 
a  concave  mirror,  and  astronomical  or  terrestrial  accord- 
ing as  it  is  designed  for  the  observation  of  celestial  or 
terrestrial  objects. 

(a)  The  astronomical  refractor  consists  essentially  of  a  large  convex 
lens  objective  of  long  focus,  and  a  convex  lens  eyepiece  of  short  focus, 


FIG.  304. 

as  is  shown  in  Fig.  304.  The  objective  is  made  large  that  it  may  collect 
many  rays,  to  the  end  that  its  real  and  diminished  image,  ab,  may  be 
so  bright  that  it  may  be  considerably  magnified  without  too  great  loss 
of  distinctness.  This  real  image  formed  by  the  objective  is  magnified 
by  the  eyepiece,  as  in  the  case  of  the  compound  microscope.  The 
visible  image  is  a  virtual  image  of  the  real  image. 

(J)    The  spy-glass  or  terrestrial  telescope  avoids  the  inversion  of  the 
image  by  the  interposition  of  two  double-convex  lenses,  m  and  n, 


408 


SCHOOL  PHYSICS. 


between  the  objective  and  the  eyepiece.  The  rays  diverging  from  the 
inverted  image  at  /  cross  between  m  and  n,  and  form  an  erect,  magni- 
fied, virtual  image  at  ab. 


FIG.  '305. 

(c)  The  Galilean  telescope  has  a  double-concave  eye-lens  that  inter- 
cepts the  rays  before  they  reach  the  focus  of  the  objective.  The  rays 
from  A,  converging  after  refraction  by  0,  are  rendered  diverging  by 


FIG.  300. 

C;  they  seem  to  diverge  from  a.  In  like  manner,  the  image  of  £  is 
formed  at  b.  The  image,  ab,  is  erect  and  very  near.  Two  Galilean 
telescopes  placed  side  by  side  constitute  an  opera-glass. 

(e?)  The  reflecting  telescope  has  as  an  objective  a  concave  mirror, 
technically  called  a  speculum.  The  images  formed  by  the  speculum 
are  brought  to  the  eyepiece  in  several  different  ways.  Sometimes  the 


FIG.  307. 


eyepiece  consists  of  a  series  of  convex  lenses  placed  in  a  horizontal 
tube,  as  shown  in  Fig.  307.     The  rays  from  the  mirror  may  be  re- 


A  FEW  OPTICAL   INSTRUMENTS.  409 

fleeted  by  a  cathetal  prism,  TOW,  and  a  real  image  formed  at  ab.  This 
image  is  magnified  by  the  eyepiece,  and  a  virtual  image  formed  at  cd. 
The  Earl  of  Rosse  built  a  telescope  with  a  mirror  that  was  six  feet  in 
diameter,  and  had  a  focal  distance  of  fifty-four  feet. 

(e)  The  magnifying  power  of  a  telescope  depends  upon  the  ratio 
between  the  focal  length  of  the  objective  and  that  of  the  eyepiece,  and 
may  be  changed  by  changing  one  eyepiece  for  another. 

Optical  Projection. 

Experiment  288.  —  Reflect  a  horizontal  beam  of  sunlight  into  a 
darkened  room.  In  its  path,  place  a  piece  of  smoked  glass  on  which 
you  have  traced  the  representation  of  an  arrow,  AB  (Fig.  308),  or 
written  your  auto- 
graph. Be  sure  that 
every  stroke  of  the 
pencil  has  cut 
through  the  lamp- 
black and  exposed 
the  glass  beneath. 
Place  a  convex  lens 

beyond  the  pane  of 

FIG.  308. 
glass,   as    at    L,   so 

that  rays  that  pass  through  the  transparent  tracings  may  be  refracted 
by  it,  as  shown  in  the  figure.  It  is  evident  that  an  image  will  be 
formed  at  the  foci  of  the  lens.  If  a  screen,  SS,  is  held  at  the  positions 
of  these  foci,  a  and  &,  the  image  will  appear  clearly  cut  and  bright. 
If  the  screen  is  held  nearer  the  lens  or  further  from  it,  as  at  Sf  or 
S",  the  picture  will  be  blurred. 

323.  The  Optical  Lantern  is  an  instrument  for  project- 
ing on  a  screen  magnified  images  of  transparent  photo- 
graphs, paintings,  drawings,  etc. 

(a)  The  light  is  placed  at  the  common  focus  of  a  concave  mirror, 
and  of  a  convex  lens  called  -the  condenser.  A  powerful  beam  of  light 
is  thus  thrown  upon  «6,  the  transparent  object,  technically  termed  a 
"  slide."  A  compound  objective,  TO,  is  placed  at  a  little  more  than  its 
fecal  distance  beyond  the  slide.  A  real,  inverted,  magnified  image  of 
the  picture  is  thus  projected  upon  the  screen,  S,  The  tube  carrying 


410 


SCHOOL  PHYSICS. 


m  is  adjustable,  so  that  the  foci  may  be  made  to  fall  upon  the  screen, 
and  thus  render  the  image  distinct.     By  inverting  the  slide,  the  image 


FIG.  309. 

is  seen  right  side  up.  Solar  and  electric  microscopes  act  in  nearly  the 
same  way,  the  chief  difference  being  in  the  source  of  light.  An  opti- 
cal lantern  is  often  called  a  magic  lantern. 

(6)  Two  matched  lanterns  placed  so  that  their  images  coincide 
constitute  a  stereopticon.  The  use  of  such  an  instrument  avoids  the 
delay  and  unpleasant  effect  of  moving  the  pictures  across  the  screen 
in  view  of  the  audience  when  the  slides  are  changed,  and  enables  the 
production  of  many  interesting  "  dissolving  "  effects-  that  are  impos- 
sible with  a  single  lantern. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Two  pieces  of  heavy  plate-glass, 
about  8  cm.  square  ;  a  small  iron  clamp ;  three  spring  clothes-pins ;  a 
spectacle-lens  made  of  quartz,  and  a  similar  one  made  of  glass. 

1.  In  a  good  light,  press  together  two  pieces  of  clean  plate  glass 
with  a  clamp  at  their  centers,  and  explain  the  appearance  of  colors  in 
the  glass. 

2.  Spring  a  clothes-pin  upon  each  of  three  corners  of  the  glass 
plates  used  in  Exercise  1,  and  support  the  plates  by  an  iron  clamp  at 
the  fourth  corner.     Let  a  beam  of  sunlight  from  the  porte-lumiere  fall 
upon  the  face  of  the  plate  so  as  to  make  the  angle  of  incidence  45°. 
Receive  the  beam  reflected  from  the  plate  upon  a  convex  lens  so  that 
an  image  of  the  opening  in  the  shutter  will  be  projected  on  the  screen. 
Vary  the  pressure  at  the  clamp,  and  explain  the  change  of  colors  on 
the  screen. 


A   FEW  OPTICAL   INSTRUMENTS.  411 

3.  Look  through  the  two  plates  of  the  tourmaline  tongs  (Fig.  295) 
at  the  bright  sky.  Turn  one  of  the  plates  in  its  supporting  ring  and 
observe  the  changes  of  brightness.  When  the  plates  are  so  adjusted 
that  the  view  through  them  is  the  darkest,  slip  successively  between 
them  a  quartz  spectacle-lens  and  a  similar  lens  made  of  glass,  noting 
the  effect  of  each,  and  explaining  the  effect  of  one. 

•4.  Project  a  solar  spectrum  upon  a  white  screen,  and  look  at  it  in- 
tently for  50  or  60  seconds.  Then  have  some  one  suddenly  cut  off 
the  light  that  yields  the  spectrum,  and  turn  up  the  lamp  or  gas-light. 
During  these  changes,  keep  your  eyes  fixed  on  the  screen  watching  for 
any  change  that  may  take  place  in  the  appearance  of  the  spectrum. 
Describe  and  explain  any  such  change  that  takes  place. 

5.  Fasten  a  thread  to  a  disk  of  paper  of  some  bright  color.     Place 
this  disk  upon  a  sheet  of  white  paper  and  in  a  strong  light.     Look 
intently  at  the  colored  disk  for  20  or  30  seconds.   Suddenly  pull  away 
the  colored  disk  without  moving  the  eye.     Describe  and  explain  the 
after-image. 

6.  While  a  friend  is  looking  intently  at  a  distant  object,  look 
obliquely  into  his  eye,  holding  a  candle-flame  on  the  other  side  of  it. 
If  the  flame  is  properly  held,  three  images  of  it  will  be  seen  ;  one 
erect  and  bright,  reflected  from  the  cornea;  another  erect  and  less 
bright,  reflected  from  the  anterior  surface  of  the  crystalline  lens ;  and 
a  third,  inverted,  reflected  from  the  posterior-surface  of   the   lens. 
When  the  eye  that  is  being  studied  changes  its  adjustment  for  the 
observation  of  an  object  held  near  it,  the  first  image  of  the  candle- 
flame  is  unchanged,  while  the  second  and  third  become  smaller,  the 
change  being  greater  in  the  second  than  in  the  third. 

7.  Close  the  left  eye  and  look  steadily  at  the  cross  below,  holding 
the  book  about  a  foot  from  the  face.   The  dot  is  plainly  visible  as  well 

*  • 

as  the  cross.  Keep  the  eye  fixed  on  the  cross  and  move  the  book 
slowly  toward  the  face.  When  the  image  of  the  dot  falls  on  the 
"  blind  spot "  of  the  eye,  the  dot  disappears.  Hold  the  book  in  this 
position  for  a  moment  and  see  if  the  changing  convexity  of  the 
crystalline  lens  throws  the  image  of  the  dot  off  the  blind  spot,  making 
the  dot  again  visible. 


CHAPTER   VI. 

ELECTRICITY  AND  MAGNETISM. 

(Ether  Physics  continued.) 

I.    GENEKAL   VIEW. 
A.    STATIC  ELECTRICITY. 

324.  Electricity  is  the  common  cause  of  a  large  variety 
of  phenomena,  including  apparent  attractions  and  repul- 
sions of  matter,  heating,  luminous  and  magnetic  effects, 
chemical  decomposition,  etc. 

(a)  The  true  nature  of  electricity  is  not  yet  well  understood.  Lit- 
tle more  can  be  said  at  this  point  than  that  it  is  the  agent  upon  which 
certain  phenomena  depend,  and  that  "  it  behaves  like  an  incompressible 
fluid  filling  all  space  and  yet  entangled  in  an  ether  that  has  the 
rigidity  necessary  to  propagate  the  enormously  rapid  and  minute 
oscillatory  disturbances  that  constitute  radiation,  while,  at  the  same 
time,  it  allows  the  free  motion  of  ordinary  matter  through  it." 

(6)  The  phenomena  of  electricity  are  generally  classified  as  static 
or  dynamic,  and  considered  under  the  heads,  frictional  electricity  or 
current  electricity.  Owing  to  their  common  cause  and  for  reasons  of 
convenience,  little  effort  will  be  made  to  maintain  the  distinction  in 
this  work. 

(c)  "Experiments  with  electricity  produced  by  friction  are  very 
beautiful  and  of  great  theoretical  interest,  but  many  of  them  are 
troublesome  to  perform,  and  their  practical  importance  is  very  small." 

Experiment  289.  —  Draw  a  silk  ribbon  about  an  inch  wide  and  a 
foot  long  between  two  layers  of  warm  flannel  and  with  considerable 
friction.  Hold  the  ribbon  near  the  wall,  and  notice  the  unusual  at- 
traction. Place  a  sheet  of  paper  on  a  warm  board,  and  briskly  rub  it 
with  india-rubber.  Hold  it  near  the  wall,  as  you  did  the  ribbon,  and 

notice  the  effect. 

412. 


STATIC   ELECTRICITY. 


413 


FIG.  310. 


Experiment  290.  —  Cut  a  number  of  pith-balls  about  1  cm.  in  di- 
ameter. Whittle  them  nearly 
round,  and  finish  by  rolling 
them  between  the  palms  of  the 
hands.  Cover  one  of  these 
balls  with  gold-leaf,  suspend 
it  by  a  silk  fiber,  and  call  it  an 
electric  pendulum.  Briskly  rub 
a  stout  stick  of  sealing-wax  with 
warm  flannel,  and  bring  it  near 
the  electric  pendulum.  Xotice 
the  attraction. 

Experiment     291.  —  To    the 

middle  of  a  straw  about  a  foot 

long,  fasten  with  wax  a  short 

piece    of    straw    as    shown    in 

Fig.  311.     Fasten  two  disks  of 

bright-colored  paper  at  the  ends 

of  the  straw,  and  balance  the 

apparatus  upon  the  point  of  a  sewing-needle,  the  other  end  of  which 
is  thrust  into  the  cork  of  a  glass  vial.  Rub  the 

Q  *  O  sealing-wax  as  before,  and  hold  it  near  one  of 

the  paper  disks.  The  straw  may  be  made  to 
follow  the  wax  round  and  round.  A  paper 

hoop  or  an  empty  egg-shell  may  be  made  to  roll  after  the  rubbed  rod. 

Experiment  292.  —  Repeat  the  last  two  experiments,  using  a  glass 

rod  or  tube  that  has  been 
rubbed  with  a  silk  pad. 
The  ends  of  the  glass 
should  be  rounded  or 
smooth;  a  long  ignition- 
tube  will  answer.  The 
effect  may  be  increased  by 
smearing  lard  on  one  side 
of  the  pad,  and  applying  a 
coat  of  the  amalgam  that 
may  be  scraped  from  bits 
FIG.  312.  of  a  broken  looking-glass. 

Small    scraps    of  paper,    shreds    of    cotton  and  silk,  feathers   and 


II 

FIG.  311. 


414 


SCHOOL   PHYSICS. 


gold-leaf,  bran,  sawdust,  and  other  light  bodies  may  be   similarly 
attracted. 

Experiment  293.  —  Place  an  egg  in  an  egg-cup,  and  balance  a  yard- 
stick upon  it.  The  end  of  the  stick  may 
be  made  to  follow  the  rubbed  rod  round 
and  round.  Place  the  blackboard  pointer 
or  other  stick  in  a  wire  stirrup  (Fig.  313) 
or  stiff  paper  loop  suspended  by  a  stout 
silk  thread  or  a  narrow  silk  ribbon.  It 
may  be  made  to  imitate  the  actions  of  the 
balanced  yardstick. 

Experiment  294.  —  Suspend  the  rubbed 
sealing-wax  or  glass  rod  in  the  stirrup, 
and  hold  the  pointer  or  your  hand  near 
it.  Evidently  the  action  is  mutual,  i.e., 
each  body  attracts  the  other. 


FIG.  313. 


325.  Electrification.  —  Bodies  that  are  endowed  with  the 
power  of  attracting  other  bodies  as  just  illustrated  are  said 
to  be  electrified.     Any  substance  may  be  electrified  by  suit- 
able means.     The  state  or  condition  thus  established  is 
called  electrification,  and  may  be  brought  about  in  a  variety 
of  ways. 

Experiment  295.  —  Support  a  meter  stick  upon  a  glass  tumbler. 
Bring  an  electrified  glass  rod  to  one  end  of  the  stick,  and  hold  some 
small  pieces  of  gold-leaf  or  paper  a  few  centimeters  under  the  other 
end  of  the  stick.  The  gold-leaf  or  paper  will  be  attracted  and  repelled 
by  the  stick  as  it  previously  was  by  the  glass  itself.  The  electrifica- 
tion passed  along  the  stick  from  end  to  end. 

326.  Conductors  and  Insulators. — Substances  that  easily 
permit  the  transference  of  electrification  along  them  are  said 
to  be  good  conductors.     No  substance  is  so  good  a  conductor 
as  not  to  offer  some  resistance  to  the  transfer.     No  sub- 
stance is  so  poor  a  conductor  that  the  electrification  cannot 
be  forced  through  it,  but  there  are  some  that  offer  resistances 


STATIC   ELECTRICITY. 


415 


Conductors. 

Salt  water. 

Metals. 
Charcoal. 

Vegetables. 
Animals. 

Graphite. 
Acids. 

Linen. 
Cotton. 

so  great  that  they  are  called  insulators,  or  non-conductors. 
A  conductor  supported  by  an  insulator  is  said  to  be  insu- 
lated. An  insulated  body  that  is  electrified  is  said  to  have 
a  charge,  or  to  be  charged. 

(a)  In  the  following  table,  the  substances  named  are  arranged  in 
the  order  of  conductivity:  — 

Dry  wood.  Glass. 

Paper.  Sealing-wax. 

Silk.  Vulcanite. 

India-rubber.  Insulators. 
Porcelain. 

(6)  The  fact  that  a  conductor  in  the  air  may  be  insulated  shows 
that  air  is  a  non-conductor.*  Dry  air  is  a  very  good  insulator  (at  least 
1026  times  as  good  as  copper),  but  moist  air  is  a  fairly  good  conductor. 
All  experiments  in  static  electricity  are,  therefore,  more  successfully 
performed  in  clear,  cold  weather  when  the  atmosphere  is  dry.  Resist- 
ance and  conductivity  will  be  'more  specifically  considered  in  subse- 
quent pages. 

(c)  A  medium  intervening  between  two  electrified  bodies,  i.e.,  a 
substance,  solid,  liquid  or  gaseous,  through  or  across  which  electric 
force  is  acting,  is  called  a  dielectric.  The  dielectric  plays  an  important 
part  in  the  phenomena  of  electrification. 


Kinds  of  Electrification 
Experiment  296.  —  Suspend  several  pith- 
balls  by  fine  linen  threads  from  an  insu- 
lating support,  and  touch  them  with  an 
electrified  rod.  The  rod  repels  the  balls, 
and  the  balls  repel  each  other. 

Experiment  297.  —  Electrify  a  suspended 
pith-ball  by  contact  with  a  rubbed  rod. 
Notice  that  the  ball  is  repelled  by  the  rod, 
and  attracted  by  the  cloth  with  which  the 
rod  was  rubbed. 

Experiment  298.  —  Bring  an  electrified 
glass  rod  near  a  pith-ball  electroscope  as 
before,  and  notice  that,  after  contact,  the 


FIG.  314. 


416  SCHOOL  PHYSICS. 

ball  is  actively  repelled.  Similarly  charge  a  second  ball  with  an 
electrified  rod  of  sealing-wax.  Bring  the  two  balls  near  each  other, 
and  notice  their  mutual  attraction.  Charge  the  two  balls  as  before. 
Bring  the  glass  rod  near  the  ball  that  is  repelled  by  the  sealing-wax, 
and  notice  the  attraction.  Bring  the  sealing-wax  near  the  ball  that  is 
repelled  by  the  glass  rod,  and  notice  the  attraction. 

327.  Opposite    Electrifications.  —  As    just    illustrated, 
electrification  may  be  manifested  by  repulsion  as  well  as 
by  attraction,  and  is  of  two  kinds,  opposite  in  character. 
The  electrification  developed  by  rubbing  glass  with  silk 
is  called  positive ;   that  developed  by  rubbing  sealing-wax 
with  flannel  is  called  negative.     Bodies  similarly  electri- 
fied repel  each  other;   bodies  oppositely  electrified  attract 
each  other. 

(a)  The  statement  that  there  are^  two  kinds  of  electrification  does 
not  necessarily  imply  that  there  are  two  kinds  of  electricity.  It  is, 
however,  very  convenient  to  speak  of  one  kind  of  electrification  as 
caused  by  a  charge  of  one  kind  of  electricity,  and  the  other  kind  of 
electrification  as  caused  by  a  charge  of  an  opposite  kind  of  electricity. 

(&)  Any  substance  mentioned  in  the  following  electric  series  is  posi- 
tively electrified  when  rubbed  with  any  substance  that  follows  it,  and 
negatively  electrified  when  rubbed  with  any  substance  that  precedes  it 
in  the  list :  — 

1.  Cat's  fur,     5.  Glass,  9.  Vrood,  13.  Resin, 

2.  Flannel,       6.  Cotton,          10.  Metals,  14.  Sulphur, 

3.  Ivory,  7.  Silk,  11.  Caoutchouc,      15.  Gutta-percha, 

4.  Quartz,        8.  The  hand,     12.  Sealing-wax,     16.  Gun-cotton. 

Thus,  cat's  fur  is  always  positively  electrified,  and  gun-cotton  nega- 
tively, when  rubbed  with  any  other  substance  mentioned  in  the  list. 
Glass  is  positively  electrified  when  rubbed  with  silk,  and  negatively 
when  rubbed  with  flannel. 

(c)  The  electrification  of  the  rubbed  body  is  equal  in  amount  to 
that  of  the  body  with  which  it  is  rubbed,  but  opposite  to  it  in  character. 

328.  Electrification    by   Conduction    is    the   process    of 
charging  a  body  by  putting  it  in  contact  with  an  electrified 


STATIC   ELECTRICITY. 


417 


body.  The  charge  thus  produced  is  of  the  same  kind 
as  that  of  the  communicating  body. 

329.  The  Electroscope  is  an  instrument  for  detecting  and 
testing  electrification.  The  electric  pendulum,  or  the  bal- 
anced straw  of  Experiment  291, 
constitutes  a  simple  and  efficient 
electroscope.  The  gold-leaf 
electroscope  represented  in  Fig. 
315  is  a  common  form  of  a  more 
sensitive  instrument.  A  metal- 
lic rod  passes  through  the  cork 
of  a  glass  vessel,  and  terminates 
on  the  outside  in  a  ball  or  a 
disk.  The  lower  end  of  the  rod 
carries  two  strips  of  gold-leaf 
or  of  aluminium-foil  that  hang 
parallel  and  close  together. 

When  an  electrified  object  is  brought  near  the  knob  or  into 
contact  with  it,  the  metal  strips  below  become  similarly 
charged  and  are,  therefore,  mutually  repelled. 

(a)  A  proof-plane  may  be  made  by  cementing  a  bronze  cent  or  a 

disk  of  gilt  paper  to  a  thin  insulating 
handle,  as  a  glass  tube  or  a  vulcanite 
rod.  Slide  the  disk  of  the  proof-plane 
along  the  surface  of  the  electrified 
body  to  be  tested,  and  quickly  bring  it 
into  contact  with  the  knob  of  the  gold- 
leaf  electroscope,  the  leaves  of  which 
will  diverge.  Positively  charge  the 
proof-plane  by  contact  with  a  glass 
rod  that  has  been  electrified  by  rub- 
bing it  with  silk,  and  transfer  the 

second  charge  to  the  electroscope.     If  the  leaves  diverge  more  widely, 
27 


FIG.  315. 


418  SCHOOL  PHYSICS. 

the  first  charge  was  positive.  If  the  leaves  collapse,  repeat  the  test, 
using  the  negative  charge  from  a  rod  of  sealing-wax  rubbed  with  flan- 
nel instead  of  the  positive  charge  from  the  glass  rod.  If  the  leaves 
are  thus  made  to  diverge  more  widely,  the  first  charge  was  negative. 

330.  Electrical  Units.  —  There  are  two  systems  of  elec- 
trical units  derived  from  the  fundamental  "  C.G.S."  units, 
one  set  being  based  upon  the  attraction  or  repulsion  ex- 
erted between  two  quantities  of  electrification,   and  the 
other  upon  the  force  exerted  between  two  magnet  poles. 
The  former  are  termed  electrostatic  units;  the  latter,  elec- 
tromagnetic units.     Distinctive  names  have  not  yet  been 
adopted  for  the  electrostatic  units. 

331.  The  Electrostatic  Unit  of  Quantity  is  the  quantity 
of  electrification  that  exerts  through  the  air  a  force  of  one 
dyne  on  a  similar  quantity  at  a  distance  of  one  centimeter. 
The  force  may  be  attractive  or  repulsive. 

332.  Law  of  Electric  Action.  —  The  force  that  is  mutu- 
ally exerted  between  two  charges  varies  directly  as  the 
product    of   the  charges,  and  inversely  as  the  square  of 
the  distance  between  them.    The  two  charges  are  supposed 
to  be  collected  at  two  points.- 


Distribution  of  the  Charge. 

Experiment  299.  —  Make  a  conical  bag  of  linen,  supported,  as  shown 
in  Fig.  317,  by  an  insulated  metal  hoop  five  or  six  inches  in  diameter. 
Electrify  the  bag.  A  long  silk  thread  extending  each  way  from  the 
apex  of  the  cone  will  enable  you  to  turn  the  bag  inside  out  without 
discharging  it.  Test  the  inside  and  outside  of  the  bag,  using  the 
proof  -plane.  Turn  the  bag  and  repeat  the  test.  Whichever  surface 
of  the  linen  is  external,  no  electrification  can  be  found  upon  the  in- 


STATIC   ELECTRICITY.  419 

side  of  the  bag.      Vary  the  experiment  by  the   use  of   a  hat  sus- 
pended by  silk  threads.     Notice  that  the 
greatest  charge    is    obtained    from    the 
edges;   less  from   a  curved  or  flat  sur- 
face ;  none  from  the  inside. 

Experiment  300.  —  Fasten  one  edge  of 
a  large  sheet  of  tin-foil  to  a  horizontal 
glass  rod  or  tube.  Connect  a  lower  cor- 
ner of  the  tin-foil  by  a  fine  wire  to  the 
knob  of  an  electroscope.  Charge  the 
tin-foil  lightly,  and  notice  the  divergence 
of  the  leaves  of  the  electroscope.  Slowly 
turn  the  rod  so  as  to  roll  the  tin-foil  upon 
it.  As  the  area  of  the  electrified  surface 
is  reduced,  notice  the  increase  in  the  divergence  of  the  leaves. 

Experiment  301.  —  Prick  a  pin-hole  at  each  end  of  an  egg,  and  blow 
out  the  contents  of  the  shell.  Paste  tin-foil  or  Dutch-leaf  smoothly 
over  the  entire  surface  of  the  empty  shell.  Fasten  the  two  ends  of 
a  white  silk  thread  with  wax  near  the  ends  of  the  shell,  so  that  the 
shell  may  be  suspended  with  its  greater  diameter  horizontal.  Charge 
this  insulated  egg-shell  conductor.  With  a  proof-plane,  carry  a 
charge  from  the  side  of  the  conductor  to  the  knob  of  the  gold-leaf 
electroscope,  and  notice  the  degree  of  divergence  of  the  leaves.  In 
like  manner,  carry  a  charge  from  the  smaller  end  of  the  conductor, 
and  notice  the  greater  divergence  jpf  the  leaves. 

Experiment  302.  —  Cement  the  end  of  a  small  glass  tube  to  the 
middle  of  a  pin,  and  hold  the  head  of  the  pin  against  the  knob  of  a 
gold-leaf  electroscope.  Observe  the  collapse  of  the  leaves. 

333.  Distribution  of  the  Charge.  — As  the  electrification 
is  self-repulsive,  the  charge  lies  wholly  upon  the  outer  sur- 
face. The  amount  of  electrification  per  unit  of  surface 
is  called  the  surface  density.  Whenever  a  charge  is  com- 
municated to  a  conductor,  the  electrification  distributes 
itself  over  the  surface  of  the  conductor  until  it  reaches  a 
condition  of  equilibrium.  A  change  in  the  area  of  the 
surface  works  a  corresponding  change  in  the  surface 


420  SCHOOL  PHYSICS. 

density,  as  was  shown  in  Experiment  300.  The  distri- 
bution is  a  function  of  the  surface,  independent  of  the 
substance  of  the  conductor,  and  greatest  where  the  curva- 
ture is  the  greatest.  On  a  sphere,  the  density  is  uniform  ; 
on  an  egg-shaped  conductor,  it  is  greatest  at  the  smaller 
end. 

(a)  Since  any  charge  is  self -repulsive,  there  must  be,  at  every  point 
of  the  surface  of  a  charged  conductor,  an  outward  pressure  against 
the  surrounding  dielectric.  The  surface  density  increases  with  the 
curvature,  but  the  repulsion  increases  still  more  rapidly,  varying  as 
the  square  of  the  density.  When  the  density  becomes  about  a 
hundred  electrostatic  units  per  square  centimeter,  the  electrification 
cannot  be  retained  upon  the  conductor,  and  sparks  fly  into  the  sur- 
rounding air.  The  discharge  takes  place  most  readily  where  the 
density  is  the  greatest;  i.e.,  where  the  curvature  is  the  greatest,  as 
at  a  point.  Since  the  air  in  contact  with  such  a  point  is  similarly 
electrified,  and,  therefore,  repelled,  an  air-current  passes  from  the 
point,  and  the  charge  is  dissipated  by  convection.  As  a  general 
thing,  points  and  sharp  edges  are  avoided  in  apparatus  for  use  with 
static  electricity,  but  they  are  sometimes  purposely  provided. 

334.  Process  of   Electrification.  —  When  two  dissimilar 
substances  are  brought  into  contact  and  then  separated,  they 
are  equally  and  oppositely  electrified.     If  the  substances  are 
poor  conductors,  they  must  be  rubbed  together  ;  i.e.,  con- 
tact must  be  made  at  every  point  in  order  to  secure  elec- 
trification over  the  entire  surface.     If  the  substances  are 
good  conductors,  the  opposite  and  equal  electrifications 
flow  to  the  point  last  in  contact,  and  pass  by  conduction 
from  one  to  the  other.     Evidently  the  resultant,  in  this 
case,  is  zero. 

335.  Electrification  and  Energy.  —  When  two  dissimilar 
substances  are  brought  into  contact,  they  become  oppositely 
electrified.     When  they  are  subsequently  separated,  work 


STATIC  ELECTRICITY.  421 

is  done  against  their  mutual  electric  attraction.  This 
work  represents  the  increased  potential  energy  of  the 
system.  That  energy  is  at  zero  when  the  bodies  are 
in  contact,  and  at  its  maximum  when  they  are  at  an  infi- 
nite distance  from  each  other.  If  the  charged  bodies  are 
similarly  electrified,  work  is  done  against  their  mutual 
electric  repulsion.  Then  the  potential  energy  of  the 
system  varies  from  zero  at  an  infinite  distance  between  the 
bodies  to  a  maximum  when  the  two  are  in  contact. 

336.  Electrical  Field  and  Lines  of  Force.  —  The  space 
surrounding  an  electrified  body  and  through  which  the  elec- 
trical force  acts  is  called  an  electrical  field  of  force.  We 
may  imagine  lines  drawn  in  this  field,  each  indicating  the 
direction  in  which  a  unit  of  electrification  would  move  if 
placed  in  the  field.  Evidently,  we  may  draw  an  indefi- 
nite number  of  such  lines,  but  in  order  to  "map"  an  elec- 
trical field  and  to  show  the  relative  intensity  of  different 
parts  of  it,  it  has  been  agreed  that  one  line  shall  be  drawn 
through  each  square  centimeter  of  surface  for  each  dyne 
of  force  exerted  in  the  field.  ""  If  one  such  line  representing 
a  force  of  one  dyne  cuts  each  square  centimeter  of  surface, 
thp  field  is  said  to  be  of  unit  intensity;  i.e.,  a  unit  of 
electrification  in  a  field  of  unit  intensity  would  be  acted 
upon  by  a  force  of  one  dyne  tending  to  move  it  along  a  line 
of  force. 

(a)  We  may  further  imagine  two  electrified  bodies  as  immersed 
in  an  electrical  field  of  force,  and  connected  by  elastic  lines  of  force 
that  tend  to  shorten  and  that  are  self-repellent.  In  such  a  field,  there 
will  be  a  stress  parallel  to  the  lines  of  force,  and  of  the  nature  of  a 
tension ;  also  a  stress  perpendicular  to  the  lines  of  force,  and  of  the 
nature  of  a  pressure. 


422  SCHOOL  PHYSICS. 

337.  Potential.  — In  a  general  way,  it  may  be  said  that 
potential  represents  degree  of  electrification,  or  that  it  is 
the  relative  condition  of  a  conductor  that  determines  the 
direction  of  a  transfer  of  electrification  to  it  or  from  it. 
The  direction  of  the  transfer  depends,  not  upon  quantity 
or  upon  surface  density,  but  upon  relative  potential. 

(a)  In  dealing  with  masses  of  matter  and  the  force  of  gravitation, 
it  is  easy  to  understand  that  the  potential  energy  of  a  unit  mass  at  a 
given  point  is  an  attribute  of  that  point,  and  that  the  condition  at  the 
point  is  due  only  to  the  existence  of  attracting  bodies,  and  is  the  same 
whether  the  unit  mass  is  actually  there  or  not.  This  attribute  of  the 
point  is  called  the  gravitation  potential  at  the  point.  The  potential  at  a 
point  is  zero  when  a  unit  particle  if  placed  there  would  have  no 
potential  energy,  as  when  the  point  is  at  an  infinite  distance  from 
all  attracting  masses.  Similarly,  if  a  charge  is  placed  anywhere  in 
an  electrical  field,  it  has  a  potential  energy  due  to  the  work  done 
upon  it  in  carrying  it  thither.  This  attribute  of  the  point  is  called  the 
electrical  potential  at  the  point.  The  charge  thus  placed  is  subject  to 
the  action  of  the  electrical  force  that  tends  to  move  it  to  another 
point  where  its  potential  energy  will  be  less;  i.e.,  to  move  it  from  a 
point  of  higher  to  a  point  of  lower  potential.  An  electrostatic  unit 
difference  of  potential  exists  between  two  points  when  an  erg  of  work  is 
involved  in  moving  unit  charge  from  one  point  to  the  other. 

(6)  Relative  potential  is  analogous  to  level.  As  the  sea-level  is 
taken  as  the  zero  from  which  altitudes  are  measured,  so  the  surface 
of  the  earth  is  taken  as  the  zero  of  electric  potential.  As  water 
tends  to  flow  from  higher  to  lower  levels,  and  as  heat  tends  to  flew 
from  places  of  higher  to  places  of  lower  temperature,  so  electrification 
tends  to  flow  from  places  of  higher  to  places  of  lower  potential  until 
an  equalization  is  reached.^  In  the  latter  case,  the  flow  is  called  a 
current  of  electricity.  If  the  quantity  of  electrification  is  limited,  the 
current  is  temporary,  as  in  the  discharge  of  a  Ley  den  jar.  If  the 
difference  of  potential  is  maintained,  the  current  is  continuous,  as  in 
the  case  of  a  voltaic  cell. 

338.  Equipotential  Surfaces.  —  Surrounding  a  unit  posi- 
tive charge  as  a  center,  there  is  a  surface  such  that  it  will 


STATIC   ELECTRICITY. 


423 


FIG.  318. 


require  the  expenditure  of  an  erg  of  work  to  carry  a  unit 
negative  charge  from  the  center  to  any  point  of  that  sur- 
face, as  from  A  to  P.  Further  from  the  center,  there  is 

another   surface    such  that   it  will 

fs'  ••>., 

require  the  expenditure  of  an  erg 
of  work  to  carry  a  unit  negative 
charge  from  the  first  surface  to  the 
second,  as  from  P  to  Q ;  i.e.,  such 
that    there    is    unit    difference    of 
potential  between  the  two  surfaces. 
Such   surfaces   as  these,   throughout 
which  the  potential  is  everyivhere  the  same,  are  called  equi- 
potential  surfaces.     Such  surfaces  are  everywhere  perpen- 
dicular to  the  lines  of  force  that  cut  the  electrical  field. 

(a)  When  a  charge  is  moved  from  any  point  to  another  point  in 
the  same  equipotential  surface,  no  work  is  done  upon  it.  When  a 

charge  is  moved  from  one  such  surface 
to  another,  the  work  done  is  indepen- 
dent of  the  path  of  transfer.  If  such 
a  surface  was  to  be  rendered  impene- 
trable, a  particle  could  lie  upon  it 
without  tendency  to  move  along  it  in 
any  direction.  If  any  two  points  in 
such  a  surface  were  to  be  joined  by  a 
conductor,  no  flow  of  electrification 
would  take  place.  The  closed  lines  in 
Fig.  319  are  equipotential  lines  drawn, 
of  course,  upon  equipotential  surfaces, 
about  two  similarly  electrified  spheres, 
the  quantity  of  electrification  at  A 
being  twice  that  at  B.  The  lines  radiating  from  A  and  B  represent 
lines  of  force. 

Experiment  303.  —  Charge  a  gold-leaf  electroscope  positively  until 
its  leaves  diverge  slightly.  Similarly  charge  a  like  electroscope  until 
its  leaves  diverge  widely.  The  potential  of  the  second  charge  is 


FIG.  319. 


424  SCHOOL  PHYSICS. 

higher  than  that  of  the  first.  Connect  the  knobs  of  the  two  electro- 
scopes by  an  insulated  conductor.  The  change  in  the  divergence  of 
the  leaves  shows  that  electrification  has  passed  from  a  place  of  higher 
to  a  place  of  lower  potential. 

339.  Electromotive  Force. — Whenever  a  positive  charge 
is  placed  upon  a  conductor,  it  raises  the  potential  at  the 
point  of  application,  and  there  is  a  flow  of  electrification 
until  the  surface  of  the  conductor  is  an  equipotential 
surface.  If  two  conductors  at  different  potentials  are 
connected  by  a  wire,  a  transfer  of  electrification  will  take 
place  until  the  difference  of  potential  disappears.  What- 
ever its  nature,  the  agency  that  tends  to  produce  such  a 
transfer  is  called  electromotive  force. 

Electrostatic  Induction. 

Experiment  304.  —  Electrify  a  glass  rod  by  rubbing  it  with  silk,  and 
bring  it  near  the  electroscope  but  without  making  contact.  The 
leaves  diverge.  When  the  rod  is  removed,  the  leaves  fall  together. 
Repeat  the  experiment,  holding  a  glass  plate  between  the  rod  and 
the  electroscope. 

Experiment  305.  —  Bring  a  metallic  sphere  positively  charged  near 
an  insulated  cylindrical  conductor  with  hemispherical  ends  and 

provided  with  pith-ball  and 
linen  thread  electroscopes  as 
shown  in  Fig.  320.  The 
divergence  of  the  pith-balls 
shows  electrification  at  the 
FIG.  320.  ends  but  not  at  the  middle 

of  the  conductor.     With  the 

proof-plane  and  gold-leaf  electroscope,  examine  the  condition  of  the 
conductor  at  the  points  A,  B,  and  m,  and  compare  your  results  with 
the  representations  in  the  figure.  Remove  the  sphere  from  the  vicinity 
of  the  conductor,  or  discharge  it  by  touching  it  with  the  hand.  All 
signs  of  electrification  on  the  conductor  disappear,  showing  that  the 
charges  at  A  and  B  were  opposite  and  equal. 


STATIC  ELECTRICITY.  425 

Experiment  306.  —  Electrify  the  insulated  conductor,  AB,  as  in  Ex- 
periment 305.  Touch  it  with  the  finger,  thus  connecting  it  with  the 
earth  and  making  it  of  indefinite  length ;  its  positive  electrification  is 
so  diffused  as  to  be  insensible.  Remove  first  the  finger  and  then  the 
electrified  sphere.  The  negative  electrification  being  no  longer  held 
at  A  by  the  attraction  of  the  positive  electrification  at  C,  diffuses 
itself  over  the  cylinder,  and  the  balls  at  each  end  of  the  cylinder 
diverge,  all  being  charged  negatively. 

Experiment  307.  —  Suspend  two  egg-shell  conductors  (see  Experi- 
ment 301),  as  shown  in 
Fig.  321.  Be  sure  that  the 
shells  are  in  contact.  Bring 
an  electrified  glass  rod  near 
one  of  them,  and  slide  one 
of  the  loops  along  the  sup- 
porting rod  until  the  shells 
are  about  10  cm.  apart. 
Hold  the  electrified  rod  be- 
tween the  shells.  It  will 

attract  one  and  repel  the  FlG  321 

other,   showing   that  they 

are  oppositely  electrified.     Bring  the  shells  into  contact  again,  and 
charge  them  similarly,  as  indicated  in  Experiment  306. 

Experiment  308.  —  Charge  one  of  the  egg-shells  of  Experiment  307, 
and  suspend  it  above  the  knob  of  a  gold-leaf  electroscope  and  at  such 
a  distance  that  the  leaves  of  the  latter  diverge  but  slightly.  Provide  a 
plate  of  beeswax  or  of  sulphur,  the  thickness  of  which  is  a  little  less 
than  the  distance  between  the  shell  and  the  knob,  and  pass  a  gas  flame 
over  its  surface  to  remove  all  electrification  from  it.  Hold  the  plate 
between  the  shell  and  the  electroscope  without  touching  either.  The 
leaves  of  the  electroscope  diverge  more  widely,  as  if  the  electric  force 
passed  more  readily  through  the  plate  than  through  the  air. 

340.  Electrification  by  Induction.  —  The  collapse  of  the 
leaves  of  the  electroscope  in  Experiment  304  showed  that 
there  was  no  transfer  of  electrification  from  the  rod  to 
the  electroscope.  Whenever  an  electrified  body  is  brought 
into  the  vicinity  of  an  unelectrified  conductor,  thus  placing 


426  SCHOOL  PHYSICS. 

the  latter  in  an  electrical  field,  and  subjecting  the  inter- 
vening dielectric  to  a  condition  of  strain,  the  unelectrified 
conductor  becomes  electrified.  A  dissimilar  electrification 
appears  on  the  side  nearer  the  electrifying  conductor,  and 
similar  electrification  upon  the  further .  side.  Electrifi- 
cation produced  in  this  way,  by  the  influence  of  an  electrified 
body  and  without  contact  with  it,  is  called  electrification  by 
induction. 

(a)  A  charged  body  surrounded  by  a  dielectric  (e.g.,  the  air)  in- 
duces an  equal  and  opposite  charge  on  the  inner  surface  of  the  en- 
closure containing  the  charged  body  and  the  dielectric  (e.g.,  the  walls 
of  the  room).  An  induced  charge  is  opposite  in  kind  to  the  charge  of 
the  inducing  body. 

(ft)  The  amount  of  inductive  effect  that  takes  place  across  an 
intervening  medium  depends  upon  the  nature  of  that  medium ;  it  is 
a  function  of  the  dielectric.  The  relative  powers  of  different  sub- 
stances to  transmit  electrical  inductive  effects  is  called  specific  inductive 
capacity,  or  the  dielectric  constant.  The  introduction  of  a  dielectric 
plate  increases  the  inductive  effect  when  the  dielectric  constant  of 
the  plate  is  greater  than  that  of  air. 

Experiment  309.  —  Charge  a  gold-leaf  electroscope  to  a  high  poten- 
tial, i.e.,  until  its  leaves  diverge  widely.  Bring  the  electric  pendulum 
of  Experiment  290,  or  a  similar  metallic  ball  similarly  suspended,  into 
contact  with  the  knob  of  the  electroscope,  and  notice  the  diminished 
divergence  of  the  leaves.  The  charge  being  distributed  over  a  larger 
surface,  the  potential  is  lowered. 

341.  The  Capacity  of  a  conductor  is  the  amount  of  elec- 
trification required  to  raise  its  potential  from  zero  to  unity, 
i.e.,  the  ratio  of  its  charge  to  its  potential.  The  unit  of 
capacity  is  the  capacity  of  a  conductor  that  requires  unit 
quantity  to  produce  unit  difference  of  potential ;  it  is 
called  a  farad;  one-millionth  of  a  farad  is  called  a  micro- 
farad. The  capacity  of  a  simple  conductor  is  dependent 
upon  its  size  and  shape,  and  upon  the  form  and  position 


STATIC  ELECTRICITY.  427 

of  neighboring  conductors  that  may  act  upon  it  induc- 
tively. 

(a)  Under  like  conditions,  the  capacities  of  spheres  are  propor- 
tional to  their  radii. 

Experiment  310.  —  Spread  a  sheet  of  tin-foil  upon  a  pane  of  glass 
supported  on  a  tumbler.     Charge  the  tin-foil  by  repeated  sparks  from . 
the  electrophorus  (§404)  until  it  will  receive  no  more.     Count  the 
number  of  sparks  that  the  tin-foil  will  receive. 

Experiment  311.  —  Lay  a  sheet  of  tin-foil  upon  the  table  so  that  it 
will  be  in  electrical  connection  with  the  earth.  Over  it  place  the  glass 
and  foil  used  in  Experiment  310.  '  Charge  the  upper  sheet  as  before, 
and  notice  that  it  will  receive  a  much  greater  number  of  sparks.  Touch 
the  lower  sheet  of  tin-foil  writh  a  finger  of  one  hand,  and  the  upper  sheet 
with  a  finger  of  the  other  hand,  thus  discharging  the  apparatus.  A 
pricking  sensation  will  be  caused  by  the  discharge. 

342.  A  Condenser  consists  of  a  pair  of  conductors  slightly 
separated  by  a  dielectric.  If  one  of  these  conductors  is 
connected  to  earth,  it  requires  a  much  larger  quantity  of 
electrification  to  raise  the  potential  of  the  other  from  zero 
to  unity,  i.e.,  the  capacity  of  the  other  is  greatly  increased. 
A  condenser  is,  therefore,  a~device  for  increasing  the  elec- 
trical density  without  increasing  the  potential,  i.e.,  for 
accumulating  a  large  charge  with  a  small  electromotive 
force.  The  smaller  the  distance  between  the  conducting 
surfaces,  the  greater  the  capacity  of  the  condenser. 

(a)  When  a  charge  is  given  to  a  conductor  on  one  side  of  the 
dielectric,  it  induces  an  opposite  charge  in  the  conductor  on  the  other 
side,  as  in  Experiment  305.  By  their  mutual  attraction,  these  op- 
posite charges  are  "bound"  at  the  surface  of  the  dielectric,  thus  leav- 
ing the  first  conductor  free  to  receive  another  charge,  which  acts 
inductively  upon  the  second  conductor  as  the  original  charge  did;  and 
so  on,  successively.  This  process  necessarily  results  in  an  increasing 
strain  of  the  dielectric ;  an  over-charge  may  break  it. 


428 


SCHOOL  PHYSICS. 


(6)  The  nature  of  the  dielectric  has  a  great  effect  on  the  capacity 
of  the  condenser.  The  specific  inductive  capacity  of  a  dielectric  may 
now  be  defined  as  the  ratio  of  the  capacity  of  a  condenser  with  air 
insulation  to  the  capacity  of  a  similar  condenser  using  the  dielectric 
in  question.  For  instance,  changing  the  dielectric  from  air  to  ebonite 
more  than  doubles  the  capacity  of  the  condenser. 

(c)  Condensers  of  the  flat  type  (Fig.  322),  consisting  of  tin-foil 

conductors  separated  by 

thin,  flat  dielectric  sheets 

(usually    of    mica),    are 

much  used.      To  obtain 

large  area,  and  hence 
great  capacity,  they  are  arranged  alternately 
in  two  series.  A  condenser  of  this  type 
(Fig.  323),  having  a  capacity  of  one  micro- 
farad, weighs  6  or  7  pounds.  The  plug- 
serves  to  connect  the  coatings  when  the  instrument  is  not  in  use. 


Fia.  322. 


FIG.  323. 


343.  The  Ley  den  Jar.  —  The  most  common  and,  for  many 
purposes,  the  most  convenient  form  of  condenser  is  the 
Leyden  jar.  This  consists  of  a  glass 
jar,  coated  within  and  without  for 
about  two-thirds  its  height  with  tin- 
foil, and  a  metallic  rod  that  communi- 
cates by  means  of  a  small  chain  with 
the  inner  coat,  and  terminates  above 
in  a  knob  or  a  disk.  The  upper  part 
of  the  jar,  and  the  wooden  or  ebonite 
stopper  that  closes  the  mouth  of  the 
jar  and  supports  the  rod,  are  generally 
coated  with  sealing-wax  or  shellac- 
varnish  to  lessen  the  deposition  of 
moisture  from  the  air.  Evidently,  it  may  be  considered 
as  a  flat  condenser  rolled  into  cylindrical  form. 

(a)  The  jar  may  be  charged  by  holding  it  in  the  hand  as  shown  in 


FIG.  324. 


STATIC  ELECTRICITY 


429 


Fig.  324,  or  otherwise  placing  the  outer  coat  in  electrical  connection 
with  the  earth,  and  bringing  the  knob  into  contact  with  a  charged 
body.  If  the  outer  coat  is  insulated  so  that  the  repelled  electrification 
cannot  pass  to  the  earth,  the  jar  cannot  be  very  highly  charged.  To 
discharge  the  jar,  pass  a  stout  wire  through  a  piece  of  rubber  tubing 
and  bend  it  into  a  V  shape,  or.  in  some  other  way,  provide  the  wire 
with  an  insulating  handle.  Bring  one  end  of  the  wire  into  contact 
with  the  outer  coat,  and  then  bring  the  other  end  into  contact  with 
the  knob.  It  is  well  to  provide  the  wire  "  discharger  "  with  metal 
balls  at  its  ends. 

(&)  That  the  phenomenon  of  electrification  pertains  to  the  dielec- 
tric and  not  to  the  conducting  plates  may  be  shown  with  a  Leyden  jar 
with  movable  coats.  The  parts  being  put  together  in  proper  order 
and  the  jar  charged,  the  inner  coat,  C,  is  re- 
moved with  a  glass  rod,  and  the  glass  vessel, 
B,  lifted  from  the  outer  coat,  A.  Tests  show 
that  A  and  C  are  not  electrified,  and  that  B  is 
electrified.  By  placing  thumb  and  forefinger 
on  the  inner  and  the  outer  surfaces  of  B,  a 
slight  shock  may  be  felt.  When  the  parts  are 
put  together,  the  condenser  is  highly  electri- 
fied, and  may  be  discharged  in  the  usual  way. 
After  a  Leyden  jar  is  discharged,  a  "residual 
charge  "  gradually  accumulates,  as  if  the  glass 
was  strained  and  slowly  returned  to  its  normal 
condition.  The  time-interval  required  for  the 
residual  charge  is  lessened  by  tapping  the  jar 
and  thus  facilitating  the  molecular  readjust- 
ments. The  metallic  coats  simply  provide  the 
means  for  the  prompt  discharge  of  the  super- 
ficial layers  of  the  molecules  of  the  dielectric. 

(c)  A  number  of  Leyden  jars  having  their 
coats  connected  constitutes  an  electric  battery. 


FIG.  325. 


344.  Nature  of  Electricity.  —  The  phenomena  of  electrifi- 
cation indicate  that  electricity  is  a  perfectly  incompres- 
sible substance  of  which  all  space  is  completely  full,  and 
the  question  arises,  is  it  not  identical  with  the  ether? 
It  has  recently  been  suggested  that  the  ether  is  made  up 


430  SCHOOL  PHYSICS. 

of  two  equal  opposite  constituents,  each  endowed  with 
inertia,  and  connected  to  the  other  by  elastic  ties  which 
the  presence  of  gross  matter  generally  weakens  and  some- 
times dissolves,  and  that  these  two  constituents  of  the 
ether  are  positive  and  negative  electricity.  According 
to  this  provisional  hypothesis,  and  the  general  belief  of 
physicists,  electricity  is  a  form  of  matter  rather  than  a  form 
of  energy.  A  full  discussion  of  the  ultimate  nature  of 
electricity  is  beyond  the  province  of  this  book,  but  it  is 
safe  for  us  to  say  that  electricity  is  that  which  is  transferred 
from  one  body  to  another  in  the  process  of  electrifying  them. 

345.  Theory  of  Electrification. — When  electricity  is 
transferred  from  one  body  to  another  and  the  bodies  are 
separated  (see  §§  334  and  335)  against  their  mutual 
attraction,  the  intervening  medium  is  thrown  into  a  state 
of  strain  indicated  by  the  lines  of  force.  This  state  of 
strain  in  the  dielectric  constitutes  electrification.  Whatever 
the  real  nature  of  electricity,  and  whether  the  phenomena 
of  attraction  and  repulsion  are  explained  on  the  hypothesis 
that  the  elastic  ether  is  strained  by  the  separation  of  the 
electrified  bodies  and  tends  to  recover  its  normal  condition, 
or  on  any  other  hypothesis,  electrification  results  from 
work  done,  and  is  a  form  of  potential  energy. 

CLASSROOM  EXERCISES 

1 .  How  can  you  show  that  there  are  two  opposite  kinds  of  electri- 
fication ? 

2.  How  would  you  test  the  kind  of  electrification  of  an  electrified 
body? 

3.  (a)  What  is  a  proof -plane  ?    (&)  An  electroscope  ?    (c)  Describe 
one  kind  of  electroscope,    (d)  Another  kind. 


STATIC   ELECTRICITY.  431 

4.  Why  do  we  regard  the  electrifications  produced  by  rubbing 
two  bodies  together  as  opposite  and  equal? 

5.  Why  is  it  desirable  that  a  glass  rod  used  for  electrification  be 
warmer  than  the  atmosphere  of  the  room  where  it  is  used  ? 

6.  Two  small  balls  are  charged  respectively  with  +  24  and  —  8  units 
of  electrification.      With  what  force  will  they  attract  one  another 
when  placed  at  a  distance  of  4  centimeters  from  one  another? 

Ans.  12  dynes. 

7.  If  these  two  balls  are  then  made  to  touch  for  an  instant  and 
then  put  back  in  their  former  positions,  with  what  force  will  they  act 
on  each  other?  Ans.  Repulsion  of  4  dynes. 

8.  At  what  distance  from  a  small  sphere  charged  with  28  units  of 
electrification  must  you  place  a  second  sphere  charged  with  56  units 
that  one  may  repel  the  other  with  a  force  of  32  dynes?        Ans.  7  cm. 

9.  (a)  Having  a  metal  globe  positively  electrified,  how  could  you 
with  it  negatively  electrify  a  dozen   globes  of  equal  size   without 
affecting  the  charge  of  the  first?   (6)  How  could  you  charge  posi- 
tively one  of  the  dozen  without  affecting  the  charge  of  the  first? 

10.  Suppose  two  similar  conductors  to  be  electrified,  one  with  a 
positive  charge  of  5  units  and  the  other  with  a  negative  charge  of  3 
units.     They  are  made  to  touch  each  other.     When  they  are  sepa- 
rated, what  will  be  the  charge  of  each? 

Ans.  One  unit  of  positive  electrification. 

11.  In  what  way  may  an  electric  charge  be  divided  into  three  equal 
parts  ? 

12.  When  a  pin  or  needle  is  held  with  its  point  near  the  knob  of  a 
charged  gold-leaf  electroscope,  the  leaves  quickly  collapse.     Explain. 

13.  A  Leyden  jar  standing  on  a  plate  of  glass  cannot  be  highly 
charged.     Why? 

14.  Will  you  receive  a  greater  shock  by  touching  the  knob  of  a 
charged  Leyden  jar  when  it  is  held  in  the  hand  or  when  it  is  stand- 
ing on  a  sheet  of  glass?    Explain. 

15.  Imagine  that  the  knob  of  a  gold-leaf  electroscope  is  connected 
by  wire  to  the  knob  of  a  Leyden  jar,  and  that  a  given  amount  of  elec- 
trification is  communicated  to  the  knob  of  the  jar.     Will  the  diverg- 
ence of  the  leaves  of  the  electroscope  be  greater  when  the  jar  is  held 
in  the  hand  or  when  it  is  standing  on  a  sheet  of  glass  ?     Explain. 

16.  Show  by  a  diagram  that  electrostatic  induction  always  precedes 
electric  attraction,  and  explain  why  the  repulsion  between  the  opposite 
electrifications  does  not  neutralize  the  attraction. 


432  SCHOOL  PHYSICS. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  rubber  comb;  metal  pipe;  tin  pail. 

1.  Quickly  pass  a  rubber  comb  through  the  hair  and  determine 
whether  the  electrification  of  the  comb  is  positive  or  negative. 

2.  Provide  an  insulated  egg-shell  conductor  as  described  in  Experi- 
ment 301,  which  the  teacher  will  electrify  by  induction,  using  a  glass  rod 
that  has  been  rubbed  with  silk  or  with  flannel.     Determine  the  kind 
of  electrification  of  the  conductor  experimentally,  and  thence  deter- 
mine theoretically  whether  the  glass  rod  was  rubbed  with  silk  or  with 
flannel. 

3.  Show  that  an  electric  charge  is  self -repulsive  by  blowing  a  soap- 
bubble  on  a  metal  pipe  and  then  electrifying  it.     Compare  the  change 
in  the  size  of  the  bubble  with  that  noticed  in  Experiment  30. 

4.  Bring  an  electrified  body  near  the  knob  of  a  gold-leaf  electro 
scope ;  touch  the  knob  with  the  finger ;  remove  the  finger ;  remove  the 
electrified  body.     Bring  a  rod  that  is  positively  charged  near  the  knob 
and,  from  the  increased  or  diminished  divergence  of  the  leaves,  deter- 
mine whether  the  electrification  of  the  first  body  was  positive  or  nega- 
tive. 

5.  Twist  some  tissue  paper  into  a  loose  roll  about  six  inches  long. 
Stick  a  pin  through  the  middle  of  the  roll  into  a  vertical  support. 
Present  an  electrified  rod  to  one  end  of  the  roll,  and  thus  cause  the 
roll  to  turn  about  the  pin  as  a  horizontal  axis.     Give  this  piece  of 
apparatus  a  scientific  name. 

6.  From  a  horizontal  glass  rod  or  a  tightly  stretched  silk  cord,  sus- 
pend a  fine  copper  wire,  a  linen  thread,  and  two  silk  threads,  each  at 
least  a  meter  long.     To  the  lower  end  of  each,  attach  a  metal  weight 
of  any  kind.     Place  the  weight  supported  by  the  wire  upon  the  disk 
of  a  gold-leaf  electroscope.     Bring  an  electrified  rod  near  the  upper 
end  of  the  wire  ;  the  gold  leaves  diverge  instantly.     Repeat  the  experi- 
ment with  the  linen  thread;   the  leaves  diverge  soon.     Repeat  the 
experiment  with  the  dry  silk  thread ;  the  leaves  do  not  diverge  at  all. 
Rub  the  rod  upon  the  upper  end  of  the  silk  thread;  no  divergence 
follows.     Wet  the  second  silk  cord  thoroughly,  and  repeat  the  experi- 
ment;  the  leaves   diverge  instantly.      Record  the   teaching   of  the 
experiment. 

7.  Prepare  two  wire  stirrups,  A  and  B,  like  those  shown  in  Fig. 
313,  and  suspend  them  by  threads.     Electrify  two  glass  rods  by  rub- 
bing them  with  silk,  and  place  them  in  the  stirrups.     Bring  A  near  B. 


CURRENT   ELECTRICITY.  433 

Notice  the  repulsion.  Repeat  the  experiment  with  two  sticks  of  seal- 
ing-wax that  have  been  electrified  by  rubbing  with  flannel.  Notice 
the  repulsion.  Place  an  electrified  glass  rod  in  A,  and  an  electrified 
stick  of  sealing-wax  in  B.  Notice  the  attraction.  Give  the  law  illus- 
trated by  these  experiments. 

8.  Place  a  gold-leaf  electroscope  inside  an  insulated  tin  pail  and 
electrify  the  pail.     Describe  and  explain  the  indications  given  by  the 
electroscope. 

9.  Insulate  a  tin  pail,  and  run  a  fine  wire  from  its  edge  to  the  knob 
of  an  electroscope.     Suspend  a  metal  ball  by  a  silk  thread,  electrify 
it,  and  lower  it  into  the  pail  without  contact.     Notice  and  account  for 
the  divergence  of  the  leaves  of  the  electroscope.     Touch  the  pail  with 
a  finger.     Notice  and  account  for  the  collapse  of  the  leaves.     Remove 
the  finger  and  withdraw  the  ball.     Notice  and  account  for  the  diver- 
gence of  the  leaves.     If  the  ball  is  negatively  charged,  what  is  the 
final  charge  of  the  electroscope? 


B.    CURRENT  ELECTRICITY. 

Experiment  312. — Partly  fill  a  tumbler  with  a  solution  made  by 
slowly  pouring  one  part  of  sulphuric  acid  into  ten  parts  of  water. 
Place  a  strip  of  zinc,  1  x  10cm.,  in  the  tumbler  of  dilute  acid,  and 
notice  the  bubbles  that  rise.  Apply  a  flame  to  them  as  they  reach  the 
surface  of  the  liquid,  and  notice  that  they  burn  with  slight  puffs. 
Hydrogen  is  evolved  by  the  chemical  action  between  the  zinc  and  the 
acid. 

Experiment  313.  —  Take  the  zinc  from  the  tumbler  of  acid  and, 
while  it  is  yet  wet,  rub  thereon  a  few  drops  of  mercury,  thus  amalga- 
mating the  zinc.  The  amalgamated  surface  will  have 
the  appearance  of  polished  silver.  Replace  the  zinc 
in  the  acid,  and  notice  that  no  bubbles  are  given  off. 
Place  a  copper  strip,  2  x  10  cm.,  in  the  solution, 
being  careful  that  it  does  not  touch  the  zinc.  No 
bubbles  appear  on  either  the  copper  or  the  zinc. 
Bring  the  strips  together  at  their  upper  ends  as 
shown  in  Fig.  326.  Bubbles  now  arise  from  the  cop- 
per. Connect  the  metals  above  the  liquid  by  a  piece 
of  copper  wire  about  No.  18.  The  same  results  are  FIG.  326. 
observed. 

28 


434 


SCHOOL  PHYSICS. 


NOTE.  —  Always  make  such  connections  secure,  metal  to  metal,  and 
with  large  area  of  contact.  Each  metal  strip  may  be  bent  at  the  top 
so  as  to  clasp  the  edge  of  the  tumbler,  leaving  the  part  on  the  inside 
long  enough  to  reach  very  nearly  to  the  bottom. 

346.  Suspicion.  —  It  seems  as  though  a  metallic  contact 
is  necessary  to  bring  about  this  phenomenon  of  bubbles  on 
the  copper.  We  have  a  complete  circuit  of  materials, 
copper  strip,  wire,  zinc  strip,  and  acid.  Perhaps  we  do 
not  see  all  that  is  taking  place  in  the  system. 

Experiment  314.  — Solder  a  wire  50  centimeters  long  to  each  strip. 
This  gives  a  better  electrical  contact  than  simply  twisting  the  wire 
about  the  strip.  Place  the  strips  in  the  acid,  and  bring  the  free  ends 
of  the  wires  into  contact  with  the  tongue,  one  above  and  one  below 
it,  being  sure  that  there  is  no  acid  on  the  wires.  A  bitter,  biting 
taste  is  felt.  Make  sure  that  this  taste  disappears  when  either  strip 
is  removed  from  the  solution ;  when  either  wire  is  disconnected  from 
the  tongue ;  or  when  the  circuit  is  broken  at  any  point. 

Experiment  315.  —  Hold  the  two  wires  over  a  compass-needle  as 
shown  in  Fig.  327.  No  change  appears.  Bring  the  two  ends  of  the 


FIG.  327. 

wire  into  contact,  and  thus  close  the  circuit.    The  needle  instantly  flies 

around  as  though  it  was  trying  to  place  itself  at  right  angles  to  the 

wire.     Break  the  circuit,  and   the   needle 

=^ N    swings  back  to  its  north  and  south  posi- 
tion.    Twist  the  wires  together,  and  bend 
the  conductor  into  a  loop  so  that  the  cur- 
rent passes  above  the  needle  in  one  direc- 
tion and  beneath  the  needle  in  the  other 
direction,  as  shown  in  Fig.  328.     The  de- 
FIG.  328.  flection  of  the  needle  will  be  greater  than 
before.     If  the  wire  is  formed  into  a  loop 
that  makes   several  turns  about   the   needle,  the  deflection  will  be 


CURRENT  ELECTRICITY. 


435 


greater  still.  Continued  investigations  with  this  simple  apparatus 
will  show  that  the  hydrogen  bubbles  cling  tenaciously  to  the  copper, 
and  that,  by  this  "polarization  of  the  cell,"  its  electrical  power  is 
much  diminished. 

Experiment  316.  —  Put  the  cover  of  a  tin  spice-box  into  a  fire  and 
thoroughly  melt  the  tin  coating  from  the  iron  plate.  The  cover  thus 
prepared  is  to  be  used  as  a  mold  for  casting  a  zinc  plate  6  mm.  thick. 
Place  the  mold  on  a  fire-shovel  and  hold  it  over  a  hot  fire,  preferably 
a  gas  or  gasoline  burner.  Fill  the  mold  with  zinc  clippings,  and 
when  they  have  melted,  place  in  the  liquid  metal  a  copper  wire  about 

28  cm.  long,  bent 

as  shown  in  Fig. 

329.       Turn    out 
FIG.  329.  the  flame  and  al-  FIG.  330. 

low  the    zinc    to 

cool.  Remove  the  zinc  plate  from  the  mold.  If  the  work  has  been 
properly  done,  the  hook  of  the  wire  will  be  embedded  in  the  zinc, 
and  the  straightened  wire  will  support  the  plate  from  its  edge  as  shown 
in  Fig.  330.  Smooth  the  rough  edges  of  the  plate  with  a  file,  and 
amalgamate  the  zinc  with  mercury. 

Invert  a  ^common  tumbler  on  a  square  board  of  soft  pine,  about 
1.5  cm.  thick,  and  large  enough  to  serve  as  a  cover  for  it.  Run  a  pen- 
cil around  the  edge  of  the  tumbler  and  draw  the  diagonals  of  the  in- 
scribed and  circumscribed  squares,  as  shown  in  Fig.  331.  Bore  holes 


FIG.  331. 


FIG.  332. 


as  shown  at  a,  &,  c,  and  d  just  large  enough  to  admit  an  electric  (arc) 
light  carbon.  Cut  four  such  carbons  to  lengths  that  are  equal  and  less 
than  the  depth  of  the  tumbler.  If  the  carbons  are  copper-coated, 


436 


SCHOOL  PHYSICS. 


FIG.  333. 


dissolve  the  copper  with  nitric  acid  from  all  of  the  rod  except 
1.5  cm.  at  the  upper  end.  Insert  one  end  of  each  carbon  into  one  of 
the  holes,  and  connect  the  four  carbons  by  a  copper  wire  as  shown  in 
Figs.  332  and  333.  Pass  the  wire  of  the  zinc  plate  through  a  small 
hole  at  the  middle  of  the  board,  so  that  the  plate  may  be  suspended 

in  the  tumbler  as  shown  in  Fig.  334. 
Wedge  the  wire  in  place.  Be  careful 
that  the  wire  from  the  zinc  does  not 
touch  the  wire  from  the  carbons  on  the 
top  of  the  cover.  It  will  be  well  to 
insulate  the  former  wire,  by  slipping 
over  it  a  piece  of  soft  rubber  tubing  of 
very  small  bore  and  two  or  three  inches 
long.  The  tubing  may  be  held  in  place 
by  a  kink  in  the  wire.  Wire  that  has 
been  insulated  with  cotton  and  paramne  may  be  used  for  supporting 
the  zinc,  the  end  that  is  to  be  embedded  in  the  zinc  being  scraped 
bare  before  the  casting. 

Prepare  a  solution  as  follows :  slowly  pour  167  cu.  cm.  of  sulphuric 
acid  into  500  cu.  cm.  of  water,  and  let  the  mixture  cool.  Dissolve 
115  g.  of  potassium  dichromate  (bi- 
chromate of  potash)  in  335  cu.  cm. 
of  boiling  water,  and  pour  the  hot 
solution  into  the  dilute  acid.  When 
this  liquid  is  cool,  fill  the  tumbler 
about  two-thirds  full  with  it,  and 
place  the  carbons  and  zinc  therein. 
Adjust  the  height  of  the  plate  as 
shown  in  Fig.  334,  and  be  sure  that 
the  zinc  does  not  touch  any  of  the 
carbons.  The  zinc  and  carbon 
should  be  kept  in  the  fluid  no  longer 
than  is  necessary.  It  is  well  to  pro- 
vide a  second  tumbler  in  which  to 
drain  them.  Each  pupil  should 
make  at  least  one  of  these  cells ;  he 
will  find  three  or  four  of  them  very  useful.  The  cost  of  the  cell  need 
not  exceed  twenty-five  cents.  Using  this  cell,  repeat  Experiment  315. 
Notice  the  direction  of  the  deflection  of  the  needle.  Reverse  the 
cell  connections,  and  notice  that  the  needle  deflects  in  the  opposite 
direction. 


FIG.  334. 


CURRENT  ELECTRICITY.  437 

347.  Certainty.  —  We  are  now  sure  that  something  un- 
usual is  going  on  in  the  wire.     This  something  is  called  a 
current  of  electricity.     Its  exact  na- 
ture is  not  yet  known,  but  much  has 

been  learned  about  its  properties  and 
the  laws  by  which  it  is  governed. 
There  is  a  difference  of  potential 
between  the  plates,  and  the  chem- 
ical action  between  the  liquid  and 
one  or  both  of  the  plates,  or  some 
other  cause,  tends  to  maintain  that 

FIG.  335. 

difference.      The  containing  vessel,  the 

plates,  and  the  exciting  liquid  constitute  a  voltaic  cell. 

348.  Direction  of  Current.  — We  cannot  conceive  a  cur- 
rent without  direction.     The  actual  direction  of  current- 
flow  is  not  known,  but,  for  the  sake  of  convenience  and 
uniformity,    electricians   assume   that    the    current   flows 
from  the  carbon  through  the  wire  to  the  zinc,  and  from 
the  zinc  through  the  liquid  to  the  carbon. 

349.  Plates,  Poles,  etc.  —  The  entire  path  traversed  by 
the  current,  including  liquids  as  well  as  solids,  is  called  the 
circuit.     The  plate  that  is  the  more  vigorously  acted  upon 
by  the  liquid  is  called   the  positive  plate  ;  the  other  is 
called   the   negative   plate.      The   free   end   of   the   wire 
attached  to  the  negative  plate  is  called  the  positive  pole 
or  electrode  ;   that  of  the  wire  attached  to  the  positive 
plate  is  called  the  negative  pole  or  electrode.     When  the 
two  electrodes  are  joined,  the  circuit  is  closed ;  when  they 
are  separated,  the  circuit  is  broken.      When  several  cells 
are  connected  so  that  the  positive  plate  of  one  is  joined 


438 


SCHOOL  PHYSICS. 


to  the  negative  plate  of  the  next,  as  zinc  to  carbon,  and  so 

on,  as  shown  in  Fig. 
336,  they  are  said  to 
be  grouped  or  joined 

c — ' — ^-  — ' —  — *-  in  series.  When  all 

z  "T"  j  (  c       of  the  positive  plates 

M^O"""  are  connected  on  one 

FlG-336'  side,   and    all    of    the 

negative  plates  are  connected  on  the  other  side,  as  shown 

in    Fig.    337,    the 

cells  are  said  to  be 

joined  in  parallel, 

or  in  multiple  arc. 

A  number  of  cells 

joined     in     either 

way  is  called  a  vol- 
taic battery. 

(a)  The  nomenclature  of  plates  and  poles  is  a  little  perplexing, 
but  the  possible  confusion  may  be  avoided  by  remembering  that  in 
any  part  of  an  electric  circuit,  a  point  from  which  the  current  flows 
is  called  positive  ( +  )  and.  a  point  toward  which  the  current  flows  is 
called  negative  (  —  ). 

NOTE.  —  The  representation  of  the  zinc  and  carbon  plates,  as  at  Z 
and  C  in  Fig.  336,  is  the  conventional  way  of  representing  a  voltaic 
cell. 

Experiment  317.  —  Provide  a  flat  piece  of  soft  pine  wood  about 
10  cm.  square  and  3  cm.  thick,  and 
wind  on  evenly  one  layer  of  No.  16 
cotton-covered  or  insulated  copper  wire, 
covering  the  whole  block.  Secure  the 
two  ends  of  the  wire  by  double- 
pointed  tacks.  Place  a  small  pocket 
compass  upon  the  block  thus  wound, 
and  turn  the  block  until  the  coils  of 
FIG.  338.  wire  are  parallel  to  the  needle  when  the 


FIG.  337. 


CURRENT  ELECTRICITY 


439 


circuit  is  open.  Then  pass  a  current  through  the  coil.  The  deflec- 
tion of  the  needle  is  much  stronger  than 
before,  although,  owing  to  the  weakening 
of  the  cell,  the  deflection  falls  off  after  a 
time.  The  instrument  we  have  made  is 
called  a  galvanoscope.  If  a  pocket  com- 
pass can  be  spared  for  this  exclusive  use, 
it  is  well  to  mount  it  in  a  grooved  block, 
and  to  attach  the  terminals  of  the  wire  to 
the  bases  of  two  binding  posts,  as  shown  in  FIG.  339. 

Fig.  339. 

Experiment  318.  — Interpose  20  feet  of  No.  30  (or  finer)  iron  wire 
in  the  circuit  of  a  voltaic  cell.  Connect  it  so  that  the  current  will 
flow  from  the  carbon  through  the  galvanoscope,  through  the  iron 


FIG.  340. 


wire,  and  back  to  the  battery.  In  other  words,  connect  the  wire 
and  galvanoscope  in  series.  The  deflection  will  be  less  than  before. 
Keep  the  current  on  just  long  enough  to  read  the  galvanoscope; 
otherwise,  the  diminished  deflection  may  be  due  more  to  the  weak- 
ening of  the  cell  than  to  the  interposition  of  the  wire. 

350.  Resistance.  —  The  interposition  of  the  iron  wire 
appears  to  diminish  the  electrical  effect,  or  to  resist  the 
current  flow.  This  property  exists  in  all  substances,  and 
its  manifestation  is  accompanied  by  a  transformation  of 
electrical  energy  into  heat.  The  property  of  a  conductor 


440  SCHOOL  PHYSICS. 

by  virtue  of  which  the  passage  of  an  electric  current  through 
it  is  diminished,  and  part  of  the  electric  energy  dissipated  is 
called  resistance. 

(a)  We  know  nothing  of  the  nature  of  electrical  resistance,  and 
perhaps  can  best  define  it,  as  we  soon  shall  (§  361,  c),  in  terms  of  dif- 
ference of  potential  and  current  strength. 

(b)  The  word  "  resistance "  is  also  applied  to  a  material   device, 
such  as  a  coil  of  wire,  introduced  into  an  electric  circuit  on  account 
of  the  resistance  that  it  offers  to  the  passage  of  the  current. 

Experiment  319.  —  Provide  20  feet  of  No.  30  iron  wire,  20  feet  of 
No.  30  copper  wire,  60  feet  of  No.  30  iron  wire,  and  20  feet  of  No.  20 

iron  wire.    Repeat  Experiment  318 


20  FT.  NO.  20.  USON 


20  FT'.  NO.  so.'  COPPER     — •z^F      with  eacn  °f  these  wires,  in  each 
BO  FT.  NO.  so.' .RON        R o .  \     case   noting  ^6  deflection  of  the 
galvanoscope,  G. 

Each  wire  may  be  coiled  on  a 
board,  care  being  taken  that  adja- 
cent coils  do  not  touch.  Coiled  or 


FIG.  341.  uncoiled,   the  wires   may  be  con- 

nected as  in  Fig.  341,  and  the  free 

end  of  F  touched  at  1,  2,  3,  and  4  successively.      Give  the  cell  a 
moment's  rest  between  successive  contacts. 

351.  The  Ohm  is  the  practical  unit  of  resistance.  It  is 
the  resistance  of  a  column  of  pure  mercury  one  square  mil- 
limeter in  cross-section  and  106.3  centimeters  long,  and  at 
a  temperature  of  0°.  A  thousand  feet  of  No.  10  copper 
wire,  or  9.3  feet  of  No.  30  copper  wire,  has  a  resistance 
of  very  nearly  an  ohm, —  an  important  "rough  and  ready" 
standard. 

(a)  The  ohm  has  been  repeatedly  determined  by  societies  and  con- 
gresses of  electricians.  The  British  Association  determined  its  mag- 
nitude with  great  care,  but  there  was  an  error  in  the  method  that 
long  passed  unnoticed.  The  international  ohm,  denned  above,  is 
equal  to  1.013+  B.A.  ohms.  Resistance  boxes  and  other  apparatus 
measuring  in  B.A.  ohms  are  common;  their  results  should  be  cor- 
rected as  above  indicated. 


CURRENT  ELECTRICITY.  441 

(6)  A  million  ohms  is  called  a  megohm ;  one-millionth  of  an  ohm 
is  called  a  microhm. 

352.  Laws  of  Resistance.  —  Three  important  laws  have 
been  experimentally  established  :  — 

(1)  Other  things  being  equal,  the  resistance  of  a  conductor 
is  directly  proportional  to  its  length. 

(2)  Other  things  being  equal,  the  resistance  of  a  conductor 
is  inversely  proportional  to  its  area  of  cross-section,  or  to 
the  square  of  its  radius  or  diameter. 

(3)  Other  things  being  equal,  the  resistance  of  a  wire  de- 
pends upon  the  material  of  which  it  is  made.     At  a  given 
temperature,  resistance  is  directly  proportional  to  a  con- 
stant that  is  different  for  different  substances. 

(a)  This  constant,  Kt  is  called  the  specific  resistance  or  the  resistivity 
of  the  material.  The  specific  resistance  of  a  substance  is  the  resistance 
at  0°  C.  of  a  cubic  centimeter  of  the  substance,  i.e.,  of  a  conductor 
made  of  the  substance,  1  cm.  long  and  1  sq.  cm.  in  cross-section.  It 
varies  widely  with  temperature  and  other  considerations,  and  is  prac- 
tically measured  in  microhms.  The  reciprocal  of  resistivity  is  called 
conductivity,  and  is  measured  in  a  unit  called  the  mho.  Tables  of 
resistances,  etc.,  are  given  in  the  appendix. 

(&)  The  laws  of  resistance  may  be  expressed  algebraically  as  fol- 
lows :  — 

**% 

in  which  R  represents  the  resistance  of  the  wire  in  ohms  ;  K,  the  resis- 
tivity of  the  material;  and  I  and  r,  the  length  and  radius  in  centi- 
meters. 

Experiment  320.  —  Heat  a  long,  fine  iron  wire  to  dull  redness  by 
an  electric  current,  and  dip  a  loop  of  the  hot  wire  into  ice-cold  water. 
The  resistance  of  the  cooled  part  of  the  wire  is  lessened,  the  current 
is  increased  thereby,  and  the  uncooled  part  of  the  wire  becomes 
highly  incandescent. 


442  SCHOOL  PHYSICS. 

353.  Effect  of  Temperature  on  Resistance.  —  The  resist- 
ance of  metals  and  of  most  other  substances  increases  as 
the  temperature  rises.  But  the  resistance  of  some  sub- 
stances, notably  carbon  and  electrolytes,  is  lowered  by 
heating.  The  "  cold  "  resistance  of  the  carbon  filament  of 
an  incandescent  electric  lamp  is  much  greater  than  the 
resistance  of  the  same  filament  when  the  lamp  is  lighted. 

(a)  Suppose  a  wire  at  any  point  to  become  reduced  to  half  its 
diameter.  The  cross-section  will  have  an  area  £  as  great  as  in  the 
thicker  part.  The  resistance  here  will  be  4  times  as  great,  and  the 
number  of  heat  units  developed  will  be  4  times  as  great  as  in  an  equal 
length  of  the  thicker  wire.  But  4  times  the  amount  of  heat  spent 
on  \  the  amount  of  metal  will  warm  it  to  a  degree  16  times  as  great. 
In  other  words,  the  heat  developed  by  a  given  current  in  different 
parts  of  a  wire  of  uniform  material  and  varying  size  is  inversely  pro- 
portional to  the  fourth  power  of  the  diameters. 

CLASSROOM  EXERCISES. 

1.  What  is  the  resistance  of  a  No.  10  copper  wire  1,000  feet  long? 
(Consult  the  table  in  the  appendix.) 

2.  What  is  the  resistance  of  800  feet  of  German  silver  wire,  No.  4  ? 

3.  What  is  the  resistance  of  750  feet  of  iron  wire,  No.  8? 

4.  What  is  the  resistance  of  350  feet  of  silver  wire,  No.  14? 

5.  What  is  the  resistance  of  6,050  feet  of  copper  wire,  No.  25? 

6.  There  is  a  "  fault "  in  a  telegraph  line  3,590  feet  long  and  made 
of  No.  14  iron  wire.     By  means  of  electrical  instruments,  it  is  found 
that  the  resistance  of  the  wire  from  one  end  to  the  fault  is  1.75  ohms. 
How  far  is  the  fault  from  the  end  of  the  line  ? 

7.  What  is  the  resistance  of  the  whole  line  mentioned  in  Exer- 
cise 6? 

.8.  How  far  away  would  the  fault  have  been,  had  the  line  been  of 
No.  14  copper  wire  ?/ 

9.  Determine  the  diameter  of  a  copper  wire  that  has  a  resistance 
of  2  ohms  per  thousand  feet. 

10.  What  is  the  resistivity  of  a  wire  50  mils  in  diameter,  900  feet 
long  and  having  a  resistance  of  46.2  ohms?  Of  what  material  men- 
tioned in  the  table  on  page  593  might  the  wire  be  made  ? 


CURRENT  ELECTRICITY. 


443 


354.  Analogy.  —  In  many  respects,  it  is  convenient  to 
compare  the  flow  of  electrification  through  a  wire  to  the 
flow  of  water  through  a  horizontal  pipe.  Such  a  compari- 
son yields  the  following  analogues  :  — 


Functions. 
Pressure. 
Quantity. 
Rate  of  flow. 

Resistance. 

Work. 

Rate  of  work. 


Hydraulic  Units. 

Head  in  feet. 

Pound. 

Pounds  per  second. 

Xo  definite  unit. 
Foot-pound. 

Foot-pounds  per  second, 
or  horse-power. 


Electromagnetic  Units. 

Volt. 

Coulomb. 

Coulombs  per  second, 

or  ampere. 
Ohm.  . 
Joule. 
Volt-ampere,  or  watt. 


355.  The  Volt.  —  Just  as  a  head  of  water  supplies  a 
hydraulic  pressure  that  causes  the  liquid  to  flow  through  a 
pipe  in  spite  of  friction,  so  there  is  an  electrical  pressure 
that  forces  a  current  through  a  conductor  in  spite  of  its 
resistance.  As  hydraulic  pressure  might  be  called  water- 
moving  force,  so  electrical  pressure  is  called  electromotive 
force  (E.M.F.).  The  unit  of  electrical  pressure  is  called 
the  volt,  and  is  almost  the  same  as  the  electromotive 
force  of  a  cell  consisting  "of  a  copper  and  a  zinc  plate 
immersed  in  a  solution  of  zinc  sulphate.  . 

(a)  The  E.M.F.  of  a  Daniell  cell  is  about 
1.1  volts ;  of  a  fresh  chromic  acid  cell,  2  volts ; 
and  of  a  Leclanche  cell,  1.5  volts.  The  E.M.F. 
of  a  Carh art-Clark  standard  cell  (see  Fig.  342)  is 
1.44  volts  at  15°;  conversely,  a  volt  is  about  0.7  of 
the  E.M.F.  of  a  Carhart-Clark  standard  cell  at  that 
temperature.  A  standard  cell  should  never  be 
used  on  a  closed  circuit. 

Experiment  321.  —  Prepare  a  block  for  a  gal- 
vanoscope,  winding  it  closely  with  ten  layers  of 
No.  34  insulated  copper  wire,  thus  making  an 


FIG.  342. 


444 


SCHOOL  PHYSICS. 


FIG.  343. 


instrument  of  high  resistance.     Arrange  a  circuit  as  shown  in  Fig. 

343,  employing  about  ten  feet  of 
No.  30  iron  wire.  As  the  copper 
wire,  /,  is  slid  along  the  iron  wire 
from  a  to  #,  the  deflection  of  the 
galvanoscope  will  decrease. 

356.  Difference  of  Potential. 

—  When  the  stop-cock  of  a 
vessel  like  that  shown  in  Fig.  344  is  closed,  water  will  stand 
at  the  same  level  in  the 
vertical  tubes,  a,  6,  and 
c.  There  is  no  differ- 
ence of  pressure  at  dif- 
ferent points  along  the 
tube  B,  and,  therefore, 
no  flow  of  water.  When 
the  stop-cock  is  opened, 
the  pressure  at  C  is  relieved,  and  the  greater  pressure  at  the 
bottom  of  A  results  in  a  flow  along  the  horizontal  pipe. 
I  c  The  variations  in  liquid 

pressure  at  different  points 
along  B  is  now  shown  by 
the  differences  of  level  in 
C  a,  b,  and  c  (Fig.  345).  The 
pressure  becomes  less  as 
we  pass  from  A  toward  C. 
The  analogous  phenome- 
non is  shown  in  Experiment  321,  where  the  galvanoscope 
reveals  the  differences  of  electric  pressure,  or  potential,  at 
different  points  of  the  circuit. 

(a)  Difference  of  potential  is  a  different  thing  from  electromotive 
force.     The  electromotive  force  of  a  circuit  is  the  total  electrical  pres- 


FIG.  344. 


FIG.  345. 


CURRENT  ELECTRICITY.  445 

sure  existing  therein,  while  the  difference  of  potential  is  merely  the 
difference  of  electrical  pressure  between  two  points  on  the  circuit.  A 
generator  of  electricity  for  arc  lights  may  have  an  electromotive  force 
of  3,000  volts,  while  the  difference  of  potential  between  the  terminals 
of  an  arc  lamp  in  circuit  with  it  is  only  45  volts. 


Experiment  322.  —  Connect  several  similar  cells  in  series,  as 
shown  in  Fig.  346.  Put  a  Xo.  40 
iron  wire,  wn,  and  a  larger  copper 
wire,  'ef,  in  circuit  as  shown.  Slide 
the  end  of  the  copper  wire  along  the 
iron  wire  from  n  toward  m  until  the 
latter  becomes  red  hot. 


HHhHHH 


357.  The   Ampere. —In  Ex- 
periment    322,     we     gradually  FIG 
reduced  the  length  of  the  cir- 
cuit, and  thus  reduced  its  resistance.     As  the  resistance 
was  reduced,  the  electromotive  force  of  the  battery  sent 
a   correspondingly   increased  current  through   the  wire. 
This  increase  of  current  strength  was  manifested  by  the 
increased  heating  effect.      The  unit  of  rate  of  flow,  or  cur- 
rent strength,  is  the  ampere,  which  may  be  defined  as  the 
current  flowing  in  unit  of- time  (second)  through  a  wire 
having  unit  resistance  (ohm),  and  between  the  two  ends  of 
which  unit  difference  of  potential  (volt)  is  maintained. 

(a)  A  1-ampere  current  passes  a  coulomb  of  electricity  each  second, 
and  will  electrolytically  deposit  0.001118  of  a  gram  of  silver,  or 
0.0003287  of  a  gram  of  copper  in  a  second.  A  thousandth  of  an 
ampere  is  a  milliampere. 

358.  The  Coulomb.  —  Just  as  quantity  of  water  may  be 
measured  in  pounds,  so  quantity  of  electrification  is  meas- 
ured in  coulombs.     The  coulomb  may  be  defined  as  the 
quantity  of   electrification   carried   past   any  point   by  a 


446  SCHOOL  PHYSICS. 

1-ampere  current  in  one  second.     The  unit  is  rather  large 
for  practical  purposes,  and  is  but  little  used. 

359.  The  Joule  is  the  electrical  unit  of  ^vork,  and  repre- 
sents the  energy  of  one  coulomb  delivered  under  a  pressure 
of  one  volt,  or  the  work  done  in  one  second  in  maintaining 
a  current  of  one  ampere  against  a  resistance  of  one  ohm. 

Joules  =  volts  x  coulombs. 
It  is  equivalent  to  107  ergs. 

360.  The  Watt  is  the  unit  of  electrical  activity  or  power, 
and  represents  the  rate  of  working  in  a  circuit  when  the 
electromotive  force  is  one  volt  and  the  current  is  one 
ampere.     One  horse-power  equals  746  watts. 

Watts  —  volts  x  amperes. 
It  is  equivalent  to  107  ergs  per  second. 

361.  Ohm's  Law.  —  Representing  current  strength  by 
C,    voltage  by  E,    and  resistance  by  R,  the  numerical  re- 
lations of  these  functions  of  an  electrical  current  are  ex- 
pressed by  the  formula, 

T>  /~f 

±\j  O 

Any  two  of  these  being  known,  the  third  may  be  found. 

(a)  Applied  to  an  electric  generator  (as  a  dynamo  or  voltaic  cell), 
we  may  represent  the  resistance  of  the  external  circuit  by  R  and  the 
internal  resistance  of  the  generator  itself  by  r.  Then 

°=^R 

Thus,  if  the  E.M.F.  of  a  chromic  acid  cell  is  2  volts,   the  internal 
resistance  of  the  cell  is  1.5  ohms,  and  the  wire  resistance  is  0.5  ohms, 


C= 


1.5  +  0.5 
The  cunrent  strength  will  be  1  ampere. 


CURRENT  ELECTRICITY.  447 

(6)  Representing  algebraically  the  definition  of  the  watt,  we  have 
W=ExC.  (1) 

Substituting,  in  this  equation,  the  above  given  value  of  E,  we  have 

W=RxC*.  (2) 

Substituting,  in  the  same  equation,  the  above  given  value  of  C,  we  have 


(c)  In  the  light  of  Ohm's  law,  resistance  might  be  defined  as  the 
ratio  between  E.  M.  Y.  and  current  strength,  or  as  electric  pressure 
divided  by  electric  flow. 

362.  Joule's  Law.  —  The  work  done  by  an  electric  cur- 
rent is  equal  to  the  product  of  the  strength  of  the  current, 
C;  the  fall  of  potential,  E;  and  the  time,  t. 

W=  CEt. 

Since,  by  Ohm's  law,  E  =  (7/2,  we  have  the  following 
equivalent  expression  :  — 

W=  C*Bt. 

If  E  is  measured  in  volts,  C  in  amperes,  and  R  in  ohms, 
W  will  be  expressed  in  joules  per  second,  or  watts. 
Since  a  small  calory  equals  4.2  joules, 


in   which   formula,*  H  represents   the   number   of   small 
calories. 

Experiment  323.  —  Join  equal  lengths  of  iron  wires  of  different 
sizes  end  to  end,  and  pass  a  gradually  increasing  current  through 
them.  The  smallest  wire  will  be  most  heated. 

Experiment  324.  —  Join,  end  to  end,  equal  lengths  of  iron  and  cop- 
per wires  of  the  same  size,  and  increase  the  current  that  passes  through 


448  SCHOOL  PHYSICS. 

them  until  the  iron  wire  is  red-hot.     Ascertain  the  thermal  condition 
of  the  copper  wire. 

Experiment  325.  —  Send  the  current  of  a  few  cells  in  series  through 
a  chain  made  of  alternate  links  of  silver  and  platinum  wires  of  the 
same  size.  The  platinum  links  grow  red-hot,  while  the  silver  links 
remain  comparatively  cool.  The  specific  resistance  of  platinum  is 
about  six  times  that  of  silver,  and  its  specific  heat  is  about  half 
as  great ;  hence,  the  rise  of  temperature  in  wires  of  equal  thickness 
traversed  by  the  same  current  is  about  twelve  times  as  great  for 
platinum  as  for  silver. 

Experiment  326.  —  Pass  a  suitable  current  through  a  long,  fine  iron 
wire,  and  thus  heat  it  to  dull  redness.  By  means  of  a  sliding  contact, 
progressively  shorten  the  iron  wire  part  of  the  circuit,  as  in  Experi- 
ment 322.  As  the  resistance  decreases,  the  current  increases,  until 
the  iron  wire  that  remains  in  circuit  is  melted. 

363.  Distribution  of  Heat  in  the  Circuit.  —  Since,  at  any 
instant,  the  current  strength  is  uniform  at  every  part  of 
the  circuit,  it  follows  from  the  last  formula  given  in  §  362 
that  the  heat  developed  in  any  part  of  the  circuit  will  be 
proportional  to  the  resistance  of  that  part  of  the  circuit. 
As  the  fall  of  potential  is  proportional  to  the  resistance, 
the  heat  energy  developed  in  any  part  of  the  circuit  is  pro- 
portional to  the  fall  of  potential  through  that  part  of  the 
circuit. 

364.  Shunts.  —  When  part  of  a  circuit  consists  of  two 


branches,  each  branch  is  said  to  be  a  shunt  to  the  other. 
The  current  flowing  through  such  a  circuit  will  divide, 


CURRENT  ELECTRICITY.  449 

part  of  it  going  one  way,  and  the  other  part  the  other 
way. 

(a)  Under  such  circumstances,  the  current  that  flows  through  the 
branches  will  be  inversely  proportional  to  the  respective  resistances 
of  the  branches.     To  illustrate,  suppose  that  the  branch  that  carries 
the  galvanometer,  G,  has  a  resistance  of  900  ohms,  and  that  the 
branch  that  carries  the  coil,  5,  has  a  resistance  of  100  ohms.      Then 
0.9  of  the  current  will  flow  through  5,  and  0.1  through  G. 

(b)  The  introduction  of  a  shunt  lessens  the  resistance  of  the  cir- 
cuit.    The  conductivity  of  the  circuit  between  a  and  b  is  the  sum  of 
the  conductivities  of  the  two  branches,  and  conductivity  is  the  re- 
ciprocal of  resistance.     Representing  the  resistance  of  the  branched 
circuit  by  R,  that  of  one  branch  by  r,  and  that  of  the  other  branch  by 
/,  we  have 

—  =  -  H —  ;  whence  R  = 

R       r     r'  r  +  r/ 

For  instance,  in  the  case  of  the  galvanometer  and  the  coil  above 
mentioned, 

R  =  90°  x  10°  =  90,  the  number  of  ohms. 
900  +  100 


CLASSROOM  EXERCISES. 

1.  A  copper  wire  is  carrying  a  5-ampere  current.    The  resistance  of 
this  wire  is  2  ohms. 

(a)  How  many  volts  are  necessary  to  force  the  current  through  the 
wire? 

Solution :  —  E  =  C  x  R  =  5  x  2  =  10,  the  number  of  volts. 
(6)  How  much  energy  is  consumed  in  the  wire  ? 

Solution  :  —  W  =  E  x  C  =  10  x    5  =  50,  the  number  of  watts ;  or 
W  =  R  x  C2  =    2  x  25  =  50,  the  number  of  watts. 

2.  An  incandescence  lamp  is  connected  with  an  electric  generator 
(dynamo)  300  feet  away  by  a  Xo.  18  copper  wire  that  is  carrying  a 
1-ampere  current.     A  fine  coil  galvanoscope,  used  as  described  in  Ex- 
periment 321,  would  show  differences  in  potential  between  the  ends  of 
the  two  wires  running  to  the  lamp,  and  between  the  two  terminals  of 
the  lamp  itself.     What  is  the  loss  of  voltage  due  to  the  line? 

29 


450  SCHOOL  PHYSICS. 

Solution :  —  The  table  of  resistances  given  in  the  appendix  shows 
that  the  resistance  of  the  600  feet  of  wire  is  3.83466  ohms. 

E=C  x  R  =  l  x  3.83466  =  3.83466,  the  number  of  volts. 

If  the  lamp  took  1  ampere  at  100  volts,  the  line  loss  would  be  nearly 
3.8  per  cent. 

3.  What  would  be  the  proper  size  of  copper  wire  to  supply  a  group 
of  lamps  400  feet  away,  and  taking  15  amperes,  so  that  the  line  loss 
shall  be  2  volts. 

Solution  :  —  The  resistance  of  the  line  would  be, 

R  =  —  =  —  =  0.1333,  the  number  of  ohms. 
C      15 

Itc  resistance  in  ohms  per  foot  must  be  (0.1333  -=-  800  =)  0.0001666, 
and  the  resistance  per  1,000  feet,  0.1666  ohms.  From  the  table,  we 
find  that  No.  2  is  the  nearest  size  of  wire. 

4.  The  wire  loss  of  an  electric  motor  is  156  watts.   If  the  resistance 
of  the  motor  is  2  ohms,  what  current  flows  ? 

Solution :  — 

W  =  R  x  C2;  C  =  <%/—  =  8.83,  the  number  of  amperes. 

5.  How  many  foot-pounds  per  minute  equal  a  watt?     A  us.  44.236. 

6.  How  many  horse-power  will  be  absorbed  by  a  circuit  of  arc 
lamps,  taking  9.6  amperes  at  2,900  volts  pressure  ? 

Ans.  37.32  H.P.,  nearly. 

7.  If  the  electric  generator  that  develops  the  current  described  in 
Exercise  6  wastes  10  per  cent,  of  the  power  delivered  to  it,  how  much 
work  was  done  upon  it?  Ans.   41.46  H.P. 

8.  A  group  of  incandescence  lamps  absorbs  21  amperes.     The  line 
loss  is  limited  to  1.5  volts. 

(a)  What  is  the  resistance  of  the  line  ?  Ans.   0.07143  ohms. 

(6)  How  many  watts  are  lost?  Ans.  31.5  watts. 

(c)  If  the  line  is  800  feet  from  source  of  supply  to  lamps,  what  is 

the  nearest  size  of  copper  wire  to  use ?  Ans.   No.  0000. 

9.  An  incandescence  lamp  absorbs  0.5  amperes  at  110  volts,  and 
gives  out  16  candle-power.      An   arc   light   absorbs    10  amperes  at 
45  volts,  and  produces  2,000  candle-power.     Which  light  is  the  more 
economical?     Determ.  ..,5  the  electrical  energy  per  candle-power  ab- 
sorbed by  each?     Ans.  Incandescence,  3.4375  watts;  arc,  0.225  watts. 

10.  Which  has  the  more  energy,  an  arc  light  generator  capable  of 


CURRENT  ELECTRICITY.  451 

delivering  10   amperes  t  at  900  volts  pressure,  or  an   electro-plating 
machine  that  produces  1,800  amperes  at  a  pressure  of  5  volts  ? 

11.  What  mechanical  horse-power  is  necessary  for  50  incandescence 
lamps,  each  taking  0.5  amperes  at  110  volts,  allowing  10  per  cent  loss 
for  transformation  from  mechanical  into  electrical  energy  ? 

Ans.  4.09  H.P. 

12.  What  energy  is  absorbed  by  a  coil  of  wire  of  23  ohms  resist- 
ance, through  which  3.5  amperes  is  flowing?  Ans.  281.75  watts. 

13.  A  coil  of  wire  of  resistance  37  ohms  is  subjected  to  a  pressure 
of  110  volts.     What  energy  is  expended?  A ns.  327.02  watts. 

14.  A  dynamo  receives  525  H.P.  of  mechanical  energy,  and  delivers 
350,000  watts  at  a  pressure  of  10,000  volts.     The  line  that  completes 
the  circuit  has  a  resistance  of  14  ohms,     (a)  Determine  the  current 
strength.      (b)   What   is  the    line    loss   in   volts?    (c)     in    watts? 
(rf)  What  is  the  efficiency  of  the  dynamo  ? 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Mercury;  sulphuric  acid;  nitric  acid; 
copper  sulphate ;  glass  tumblers ;  porous  cup ;  a  zinc  and  a  copper  plate ; 
sheet  lead ;  sheet  iron  ;  tin-plate ;  galvanoscope. 

1.  Put  the  cell  described  in  Experiment  313,  with  clean  and  unamal- 
gamated  plates  into  circuit  with  a  galvanoscope.  Xotice  the  move- 
ment of  the  needle,  tap  the  galvanoscope  lightly,  and  record  the 
position  in  which  the  needle  comes  to  rest.  Observe  for  a  minute 
what  takes  place  at  the  surface  of  .each  plate.  Amalgamate  the  zinc 
plate,  carefully  remove  any  adhering  mercury  drops,  replace  the  zinc 
in  the  acid,  being  careful  that  it  is  as  far  from  the  copper  as  it  was 
before.  When  the  circuit  is  again  closed  through  the  galvanoscope, 
record  the  deflection  of  the  needle,  and  observe  for  a  minute  what  takes 
place  at  the  surface  of  the  plates.  At  intervals  of  two  minutes,  record 
the  successive  deflections  of  the  needle.  If  any  bubbles  are  visible  on 
either  or  both  of  the  plates  at  the  end  of  ten  minutes,  rub  them  off 
without  removing  the  plates  from  the  acid.  Take  care  that  no  mercury 
comes  in  contact  with  the  copper,  and  record  the  deflection  of  the 
needle.  Remove  the  copper  plate  from  the  acid,  rub  it  thoroughly, 
replace  it  in  the  acid,  and  record  the  deflection  of  the  needle.  Remove 
the  copper  plate  again,  dip  it  into  nitric  acid,  and  amalgamate  it.  Put 
it  back  into  the  acid,  and  record  the  deflection  of  the  needle.  Record 
the  teachings  of  your  experiment. 


452  SCHOOL  PHYSICS. 

2.  Solder  one  end  of  50  cm.  of  insulated  copper  wire,  No.  20,  to  one 
end  of  a  zinc  plate   10  cm.  long,  2.5  cm.  wide,  and  0.5  cm.  thick. 
Similarly,  solder  a  like  wire  to  a  piece  of  sheet  copper  10  cm.  square. 
Weigh  the  plates  and  their  wires  carefully  to  0.1  of  a  gram.     Put 
the  zinc  plate  into  a  porous  cup  about  10  cm.  deep  and  4  cm.  wide, 
and  nearly   fill  the  cup  with  dilute  sulphuric   acid.     Put  the   cup 
into  a  glass  tumbler  about  10  cm.  deep  and  8  cm.  wide.     Pour  a  satu- 
rated solution  of  copper  sulphate  into  the  tumbler  until  it  stands  at 
the  same  level  as  the  acid  in  the  cup.     Amalgamate  the  zinc,  and  put 
it  back  into  the  acid.     Clean  the  copper  plate,  bend  it  so  that  it  will 
partly  encircle  the  porous  cup,  and  put  it  into  the  copper  sulphate 
solution.     Put  the  cell  into  circuit  with  a  low  resistance  galvanoscope. 
Watch  carefully  for  bubbles  on  this  copper  plate.     Record  the  deflec- 
tion of  the  needle  at  intervals  of  five  minutes  for  half  an  hour.     Take 
the  cell  to  pieces  and  clean  its  several  parts.     Weigh  the  plates  care- 
fully as  before.     Name  the  cell,  and  compare  the  constancy  of  its  cur- 
rent with  that  of  the  cell  used  in  Exercise  1.     Account  for  any  change 
in  the  weight  of  either  plate. 

3.  Cut  2  x  10  cm.  strips  of  zinc,  lead,  iron,  copper,  and  tin-plate,  and 
provide  a  carbon  plate  or  half  of  an  electric  light  carbon  rod,  and 
attach  to  each  a  copper  wire  40  or  50  cm.  long.     Successively  use  dif- 
ferent pairs  of  these  as  plates  of  similar  voltaic  cells,  connect  each  cell 
with  the  galvanoscope,  determine  and  record  the  direction  of  the  cur- 
rent and  the  magnitude  of  the  deflection,  and  make  as  many  different 
combinations  as  possible.     Arrange  the  given  materials  in  an  electro- 
motive series,  i.e.,  so  that  if  any  two  are  used  as  plates  of  a  voltaic  cell, 
the  current  will  flow  through  the  wire  from  the  former  to  the  latter. 
When  the  series  is  completed,  using  dilute  sulpuric  acid  as  the  excit- 
ing liquid,  go  over  the  work  again  using  a  dichromate  solution,  and 
ascertain  whether  any  change  in  the  series  is  required. 

4.  Wind  four  or  five  layers  of  No.  20  insulated  copper  wire  upon  the 
edge  of  a  board  25  cm.  square.     Slip  the  wire  from  the  board,  and  tie 
together  the  several  turns  of  the  wire  at  the  corners  of  the  rectangle. 
Bend  one  end  of  the  wire  into  a  hook  and  solder  it  to  the  middle  of  the 
pointed  half  of  a  sewing-needle  as  shown  at  m  in  Fig.  348.     Straighten 
the  other  end  at  a  right  angle, as  shown  at  n.     Bend  a  narrow  strip  of 
brass  at  a  right  angle,  and  in  one  arm  make  an  indentation  that  will 
hold  a  globule  of  mercury.     Support  the  brass  L  with  the  indented 
arm  horizontal,  and  from  it  hang  the  wire  rectangle.     A  globule  of 
mercury  insures  a  good  connection  at  m,  and  the  straightened  part  of 


CURRENT  ELECTRICITY. 


453 


the  wire  dips  into  a  cup  of  mercury  at  n.  Adjust  the  form  of  the  sup- 
porting hook  so  that  the  sides  of  the  rectangle  are  vertical  or  hori- 
zontal, and  place  the  face  of  the 
rectangle  in  a  north  and  south 
plane.  Pass  the  current  of  a  bat- 
tery of  3  cells  through  the  appara- 
tus, and  notice  that  the  rectangle 
turns  into  an  east  and  \vest  plane. 
Reverse  the  current  and  notice 
the  effect.  Make  a  record  of 
this  motion  of  the  wire  rec- 
tangle, and  reserve  it  for  future 
study. 

5.  Wind  four  or  five  layers  of 
No.  20  insulated  copper  wire  upon 
the  edge  of  a  board  10  x  20  cm. 
Slip   the   wire   from   the    board, 

and  tie  as  directed  in  Exercise  4.  FIG.  348. 

Place  this  coil  in  the  circuit  be- 
tween the  battery  and  the  mercury  cup  at  n,  Fig.  348.  Call  the 
larger  wire  rectangle  A,  and  the  smaller  one  B.  Hold  B  with  one 
of  its  20  cm.  sides  vertical  and  near  one  side  of  A.  Record  the  effect 
as  manifested  by  the  motion  of  .4,  when  the  current  flows  upward 
through  the  adjacent  sides  of  the  two  rectangles ;  when  the  current 
flows  downward  through  both  ;  and  when  it  flows  upward  in  one  and 
downward  in  the  other.  Formulate  a  general  expression  of  the  ac- 
tion of  parallel  currents  upon  each  other,  (a)  When  they  flow  in 
the  same  direction.  (&)  When  they  flow  in  opposite  directions.  The 
consideration  of  the  interaction  between  currents  as  herein  illustrated 
constitutes  the  subject-matter  of  electrodynamics. 

6.  Hold  the  rectangle  B  of  Exercise  5  within  A  so  that  a  long  side 
of  the  former  makes  an  angle  with  the  lower  side  of  the  latter.    Record 
the  effect.     Change  the  angle  several  times,  recording  the  effect  in 
each  case.     Formulate  a  general  expression  for  the  mutual  action  of 
currents  that  are  not  parallel  (a)  when  they  flow  toward  the  point  of 
intersection  or  from  it ;  (b)  when  one  flows  toward  the  intersection 
and  the  other  from  it. 

7.  Wind  some  Xo.  16  insulated  copper  wire  into  a  close  spiral  about 
4  cm.  in  diameter  and  15  cm.  long.     Bend  its  ends  as  indicated  in 
Fig.  349.     Put  it  into  the  circuit  of  the  battery  as  directed  for  the 


454  SCHOOL  PHYSICS. 

rectangle   of  Exercise  4  and  hold  a  bar  magnet  near  one  of  its 

ends.      Trace   the  current  through  the 
solenoid. 

8.  Pass  two  stout  copper  wires  sepa- 
rately through  a  cork  about  2  cm.  in 
diameter.  About  2  cm.  from  the  smaller 
end  of  the  cork,  connect  the  copper  wires 
with  a  short  piece  of  very  fine  iron  wire. 
FIG.  349.  Wrap  the  edge  of  a  strip  of  paper  about 

5  cm.  wide  around  the  cork  so  as  to  make 

a  paper  cup  with  the  iron  wire  inside.  Fill  the  cup  with  fine  gun- 
powder, and  close  the  other  end  with  a  cork  or  a  paper  cap.  Place 
this  torpedo  at  a  safe  distance,  connect  it  by  stout  copper  wires  to 
a  voltaic  battery,  and  send  through  the  wires  a  current  that  will 
heat  the  iron  wire  and  explode  the  torpedo.  State  some  industrial 
application  of  electricity  that  is  illustrated  by  this  exercise.  Cut  the 
leading  wires  at  three  or  four  points  and  join  them  with  short  pieces 
of  fine  iron  wire.  Tie  the  fuse  of  a  fire-cracker  around  each  piece  of 
iron  wire,  and  send  a  current  that  shall  ignite  all  of  the  fuses. 

9.  Make  a  torpedo  similar  to  the  one  described  in  Exercise  8.  In- 
stead of  interposing  the  high-resistance  iron  wire,  bend  the  copper 
wires  until  their  ends  nearly  but  not  quite  touch.  Place  the  torpedo 
at  a  safe  distance,  lay  leading  wires,  and  explode  the  torpedo  by  a 
spark  from  an  induction  coil  or  an  electric  machine  (§§  403,  405). 


C.   MAGNETISM. 

Experiment  327.  —  Wrap  a  piece  of  writing  paper  around  a  large 
iron  nail,  leaving  the  ends  of  the  nail  bare.  Wind  fifteen  or  twenty 
turns  of  stout  copper  wire  around  this  paper  wrapper,  taking  care 
that  the  coils  of  the  wire  do  not  touch  each  other  or  the  iron.  It  is 
well  to  use  insulated  wire.  Put  this  spiral  into  the  circuit  of  a  voltaic 
cell,  and  dip  the  nail  into  iron  filings.  Some  of  the  filings  will  cling 
to  the  ends  of  the  nail  in  a  remarkable  manner.  Upon  breaking  the 
circuit,  the  nail  instantly  loses  its  newly  acquired  power,  and  drops  the 
iron  filings. 

Experiment  328.  —  Draw  a  sewing-needle  four  or  five  times  from 
eye  to  point  across  one  end  of  the  nail  of  Experiment  327,  while  the 
current  is  flowing  through  the  wire  wound  upon  it.  Dip  the  needle 


MAGNETISM.  455 

into  iron  filings.  Some  of  the  filings  will  cling  to  each  end  of  the 
needle.  - 

Experiment  329.  —  Cut  a  thin  slice  from  the  end  of  a  vial  cork  and, 
with  its  aid,  float  the  needle  of  Experiment  328  upon  the  surface  of 
water.  The  needle  comes  to  rest  in  a  north  and  south  position.  Turn 
it  from  its  chosen  position  and  notice  that,  after  each  displacement,  it 
resumes  the  same  position,  and  that  the  same  end  of  the  needle  always 
points  to  the  north. 

Experiment  330.  —  Break  the  tangs  from  a  few  flat,  worn-out  files. 
Smooth  the  ends  and  sides  of  the  files  on  a  grind-stone.  Get  some 
good-natured  dynamo  tender  to  magnetize  these  hard-steel  bars  and 
three  or  four  stout  knitting-needles.  You  can  magnetize  the  needles 
yourself  by  winding  upon  them  successively,  evenly,  and  from  end  to 
end,  a  layer  of  insulated  Xo.  20  wire,  and  sending  a  current  from  a 
voltaic  battery  through  the  wire.  Freely  suspend  these  permanent 
magnets  at  a  considerable  distance  from  each  other  and  so  that  each 
can  turn  in  a  horizontal  plane.  The  knit- 
ting-needles may  be  thrust  through  two 
corners  of  triangular  pieces  of  paper  to  the 
third  corner  of  which  the  end  of  a  horse- 
hair is  fastened  by  wax.  The  heavier  mag- 
nets may  be  placed  in  stout  paper  stirrups 
similarly  supported,  or  they  may  be  floated  „ 

upon  water,  as   shown   in    Fig.    350.      The 

suspended  magnets  will  come  to  rest  in  a  north  and  south  line.  Mark 
the  north-seeking  end  of  each  magnet  so  that  it  may  be  distinguished 
from  the%other. 

Experiment  331.  —  Suspend  a  bar  of  iron  as  you  did  the  magnets  in 
Experiment  330.  Bring  one  end  of  a  magnet  near  one  end  of  the 
iron  bar,  and  notice  the  attraction.  Try  the  other  end  of  the  iron  bar. 
Bring  the  other  end  of  the  magnet  successively  near  the  two  ends  of 
the  iron  bar,  noticing  the  effect  in  each  case. 

365.  A  Magnet  is  a  body  that  has  the  property  of  attract- 
ing iron  or  steel,  and  that,  when  freely  suspended,  tends  to 
take  a  definite  position,  pointing  approximately  north  and 
south. 


456  SCHOOL  PHYSICS. 

(a)  One  of  the  most  valuable  iron  ores  is  called  magnetite  (Fe3  O4). 
Occasional  specimens  of  magnetite  attract  iron.  Such  a  specimen  is 
called  a  lodestone.  It  is  a  natural  magnet. 

(&)  Artificial  magnets  have  all  the  properties  of  natural  magnets, 
and  are  more  powerful  and  convenient.     They  may  be  temporary  or 
permanent.     Temporary  magnets  are  made  by  passing  electric  cur- 
rents around  soft  iron,  as  in  Experiment  309,  and  are  called  electro- 
magnets.    Permanent  magnets  are  made  of  hardened  steel,   as   in 
Experiment  328.     The  most  common  forms  of  artificial  magnets  are 
the  bar  magnet  and  the  horseshoe  magnet.    The  first  of  these  is  a  straight 
bar  of  iron  or  steel ;  the  second  is  U -shaped, 
as  shown  in  Fig.  351.     Several  similar  thin 
steel  bars,  separately  magnetized  and  fas- 
tened together  side  by  side  and  with  like 
poles  in    contact,   constitute   a  compound 
magnet.      A   piece  of  iron   placed   across 

the  two  ends  of   a  horseshoe  magnet  is   called   an   armature.     The 
process  of  making  a  magnet  is  called  magnetization. 

366.  Magnetic  Substances.  —  It  appears  to  be   clearly 
established   that   all   matter   is   subject  to  the  magnetic 
force  as  universally  as  it  is  to  the  force  of  gravitation. 
Substances  that  are  attracted,  as  iron  is,  are  called  para- 
magnetic ;  substances  that  are  repelled,  as  bismuth  is,  are 
called  diamagnetic.     Paramagnetic   substances  are  some- 
times called  magnetic.     Diamagnetic  substances  are  more 
numerous    than   paramagnetic    substances  ;    diamagnetic 
effects  are  more  feeble  than  paramagnetic  effects. 

367.  Magnetic  Poles.  —  When  a  bar  magnet  is  dipped 
into  iron  filings,  the  magnetic  effect  is  seen  to  be  at  maxi- 
mum at  the  ends   of   the    bar,  and   to   diminish  rapidly 
toward  the  middle,  at  which  point  no  filings  are  sustained 
(see  Experiment  328).     The  ends  of  the  freely  suspended 
magnet  also  point  toward  the  poles  of  the"  earth.      These 
ends  of  the  magnets  are  called  poles,  and  the  magnet  is  said 


MAGNETISM.  457 

to  exhibit  polarity.  A  distinguishing  mark  is  put  on  the 
end  that  turns  toward  the  north,  and  that  end  is  called 
the  marked,  north-seeking,  or  +  pole.  The  other  end  is 
called  the  unmarked,  south-seeking,  or  —  pole.  A  unit 
magnetic  pole  is  a  pole  that  exerts  a  force  of  one  dyne  upon 

a  like  pole  at  a  distance  of  one  centimeter. 

i 

(a)  For  purposes  of  discussion,  a  theoretical  magnet  is  assumed, 
long  and  indefinitely  thin  and  uniformly  magnetized.  Such  a  magnet 
may  be  looked  upon  as  a  pair  of  poles  united  by  a  bar  exerting  no 
action,  the  whole  magnetic  effect  being  concentrated  at  the  poles. 
When  it  is  freely  suspended,  the  line  that  joins  the  poles  is  called 
the  magnetic  axis. 

Magnetic  Needles. 

Experiment  332.  —  Repeat  Experiment  29  using  the  sewing-needle 
of  Experiment  329.  The  needle  will  assume  a  north  and  south 
position. 

Experiment  333.  —  Straighten  a  piece  of  watch-spring  about  15  cm. 
long  by  drawing  it  between  thumb  and  finger.     Heat  the  middle  of 
this  steel  bar  to  redness  in  a  flame  and  bend  it  double.     Bend  the 
ends  back  into   a  line  with   each   other,  as 
shown  in  Fig.  352.     Magnetize  each  end  sepa- 
rately and  oppositely.     Wind  a  waxed  thread 
around  the  short  bend  at  the  middle  to  form 
a  socket,  and  balance  the   needle   upon   the  FIG  352 

point  of  a  sewing-needle  thrust  into  a  cork. 

A  little  filing,  clipping,  or  loading  with  wax  may  be  necessary  to 
make  it  balance.  The  needle  will  point  north  and  south. 

Experiment  334.  — Pass  a  knitting-needle  through  a  small  cork 
from  end  to  end  and  so  that  the  cork  shall  be  at  the  middle  of  the 
needle.  Thrust  a  sewing-needle  or  half  of  a  knitting-needle  through 
the  cork  at*  right  angles  to  the  knitting-needle  to  serve  as  an  axis  of 
support.  Place*  the  ends  of  the  axis  upon  the  edges  of  two  glass 
goblets  or  other  convenient  objects.  Push  the  knitting-needle  through 
the  cork  until  it  balances  upon  the  axis  like  a  scalebeam.  Magne- 


458 


SCHOOL  PHYSICS. 


tize  the  knitting-needle,  and  notice  that  the  marked  end  seems  to 
have  become  heavier. 

368.  Magnetic  Needles.  — A  small  bar  magnet  suspended 
in  such  a  manner  as  to  allow  it  to  assume  its  chosen  position 
relative  to  the  earth  is  a  magnetic  needle. 

(a)  The  needle  may  turn  in  a  horizontal  or  in  a  vertical  plane.  It 
it  turns  freely  in  a  horizontal  plane,  it  is  a  horizontal  needle;  e.g., 

the  mariner's  or  the  surveyor's  com- 
pass. If  it  turns  freely  in  a  vertical 
plane,  it  constitutes  a  dipping-needle 
(Fig.  353). 
A  magnetized 
sewing-needle, 
suspended  at 
its  center  of 
mass  by  a  fine 
thread  or  hair 


FIG.  354. 


or     an     u  n- 

twisted     fiber 

will  serve  as  a 

dipping-needle.    Two  magnets  fastened 

to  a  common  axis  and  with  their  poles 

reversed  constitute  an   astatic   needle 

(Fig.  354) .    An  astatic  needle  assumes 

no  particular  direction  with  respect  to  the  earth  if  the  two  needles 

are  equally  magnetized. 


FIG.  353. 


Magnetic  Field. 

Experiment  335.  —  Lay  a  bar  magnet  on  the  table  between  two 
wooden  strips  of  the  same  thickness  as  the  magnet.  Cover  the  mag- 
net with  a  sheet  of  paper  or  cardboard,  or  a  plate  of  glass.  With 
a  dredge-box  or  muslin  bag,  sprinkle  uniformly  over  the  plate  the 
finest  filings  of  wrought  iron  that  you  can  obtain.  Gently  tap 
the  plate  to  facilitate  the  movement  of  the  filings.  They  will 
arrange  themselves  in  lines  that  seem  to  proceed  from  the  poles,  to 
curve  outward  through  the  air,  and  to  complete  their  circuit  through 
the  magnet,  as  shown  in  Fig.  355.  Place  a  short  magnet  (e.g.,  a  piece 


MAGNETISM. 


459 


of  a  magnetized  sewing-needle  suspended  by  a  silk  fiber)  just  above 
the  filings,  and  move  it  into  different  positions.     At  every  point,  the 


"""' '"  •V;-'--^--^-:-  •   -".::. ./--;•.•.•-:•:•;.;/;.':•:;:••  •.l>.>-.iPV::;iif 


FIG.  355. 

magnet  will  place  itself  parallel  to  a  tangent  to  the  curves,  with  its 
marked  end  always  pointing  in  the  same  direction  relative  to  the 
curves. 

Experiment   336.  —  Similarly  map  out  the  "magnetic  phantom" 


^^^gvjgp'- 

FIG.  356. 

curves  when  the  opposite  poles  of  two  bar  magnets  are  brought  near 
each  other.    The  result  will  be  like  that  represented  in  Fig.  356.    The 


460  SCHOOL  PHYSICS. 

lines  from  one  magnet  seem  to  interlock  with  those  from  the  other  as 
if  by  mutual  attraction. 

Experiment  337.  —  Similarly  produce  the  phantom  when  the  like 
poles  of  two  bar  magnets  are  brought  near  each  other.     The  result 


will  be  like  that  represented  in  Fig.  357.     The  lines  now  seem  to 
repel  each  other. 

369.  Magnetic  Field  and  Lines  of  Force.  —  The  space 
surrounding  a  magnetized  body  and  through  which  the 
magnetic  force  acts  is  called  a  magnetic  field.  The  iron 
filings  could  not  have  arranged  themselves  in  their  definite 
phantom  curves  except  under  the  action  of  some  force  or 
forces.  We  may  imagine  lines  drawn  in  the  magnetic 
field,  each  indicating  the  direction  in  which  a  marked  pole 
would  move.  Such  lines  are  called  magnetic  lines  of  force. 
They  are  assumed  to  flow  from  the  marked  to  the  un- 
marked pole  outside  the  magnet,  and  in  the  opposite 
direction  inside  the  magnet,  so  as  to  form  closed  loops, 
or  complete  circuits.  By  agreement  among  physicists,  as 
many  lines  are  drawn  through  each  square  centimeter 


MAGNETISM.  461 

of  surface  as  there  are  dynes  in  the  force  of  that  part  of 
the  field.  Each  line,  therefore,  represents  a  force  of  one 
dyne,  and  the  closeness  of  the  lines  indicates  the  intensity 
of  the  field. 

(a)  A  number  of  lines  of  force  traversing  a  magnetic  field  is  called 
a  flow  or  Jinx  of  force.     The  unit  of  Jinx  is  called  a  weber,  and  represents 
one  line  of  force.     A  flux  of  10,000  lines  of  force  would  be  a  flux  of 
10,000  webers.     The  unit  of  strength  of  field,  or  intensity  of  flux,  is  called 
a  gauss,  and  represents  the  number  of  lines  of  force  per  square  centi- 
meter.      With  a  flux  of  24,000  w:ebers  in  12  square  centimeters,  the 
intensity  of  flux  would  be  2,000  gausses.     A  field  is  of  unit  strength 
when  a  unit  magnetic  pole  placed  in  it  is  acted  upon  with  a  force  of 
one  dyne.     A  pole  which   when  placed  in  a  field  of  unit  strength, 
is  acted  upon  by  a  force  of  one  dyne  is  sometimes  said  to  be  of  unit 
magnetic  mass. 

(b)  By  agreement,  the  direction  in  which  a  marked  pole  would 
move  in  a  field  is  called  positive.     When  a  magnet  is  placed  in  a 
magnetic  field,  the  marked  pole  tends  to  move  in  a  positive  direction, 
and  the  unmarked  pole  in  a  negative  direction.     The  total  effect  is 
that   of   a   couple,  and   tends   to  produce    rotation.      The   universal 
tendency  of  a  magnetic  needle  thus  to  turn  upon  its  pivot  so  as  to 
place  its  axis  in  a  north  and  south  line  indicates  that  the  earth  is 
surrounded  by  a  magnetic  field. 

(c)  The  magnetic  action  that  takes  place  in  a  magnetic  field  has 
been  happily  illustrated  by  supposing  the  lines  of  force  to  be  stretched 
elastic   threads   that   tend  to  shorten   along  their  lengths,  and  that 
are  self-repellent.     Compare  §  336  (a).     This  conception  of  magnetic 
lines   of   force    suggests    that    unlike    poles   ought    to    attract   each 
other  (see  Fig.  356),  and  that  like  poles  ought  to  repel  each  other 
(see  Fig.  357). 

(</)  The  magnetic  lines  of  force  form  closed  circuits,  passing 
through  the  air  from  one  pole  to  the  other.  The  shorter  the  air- 
path,  the  more  numerous  the  lines  of  force.  Hence,  the  advantage 
of  the  U-snaPed  or  horseshoe  magnet.  When  a  bar  of  soft  iron  is 
placed  across  the  poles,  the  magnetic  circuit  is  all  iron,  and  the  lines 
of  force  that  traverse  it  are  at  a  maximum. 

(e)  A  magrretic  pole  tends  to  repel  its  own  magnetization,  to 
develop  opposite  polarities  there,  and  thus  to  weaken  itself.  To 


462  SCHOOL  PHYSICS. 

maintain  the  strength  of  the  magnet,  an  armature  is  used  to  connect 
opposite  poles,  and  thus  to  provide  a  closed  circuit  of  magnetic  mate- 
rial. Two  bar  magnets  placed  near  each  other  in  reversed  position 
may  be  given  a  closed  magnetic  circuit,  and  thus  preserved,  by  placing 
two  armatures  at  their  ends. 

Experiment  338.  —  Place  the  end  of  a  bar  magnet  upon  a  thin 
plate  of  glass,  and  bring  a  few  tacks  to  the  under  side  of  the  plate. 
The  magnetic  lines  of  force  seem  to  pass  readily  through  the  glass ; 
the  attraction  is  not  perceptibly  weakened.  In  like  manner,  try 
paper,  mica,  sheet  zinc,  and  sheet  iron.  The  paramagnetic  iron  seems 
to  act  as  a  magnetic  screen ;  the  other  substances  do  not. 

370.  Magnetic  Transparency.  —  Substances  other  than 
those   that    are    paramagnetic    allow   the    free   action   of 
magnetic  forces  through  them.      This  quality  is  some- 
times called  magnetic  transparency. 

Experiment  339.  —  Suspend  one  of  the  bar  magnets  at  a  consider 
able  distance  from  the  others.  Bring  one  end  of  another  magnet  held 
in  the  hand  near  one  end  of  the  suspended  magnet,  and  notice  the 
attraction  or  repulsion.  Also  notice  the  designations  of  the  poles  that 
are  brought  into  proximity.  Satisfy  yourself  that  — 

N  repels  X,  '  N"  attracts  S, 

S  repels  S,  S  attracts  N. 

371.  Law  of  Magnetic  Poles.  —  (1)  Like  magnetic  poles 
repel  each  other  ;  unlike  magnetic  poles  attract  each  other. 

(2)  The  force  exerted  at  different  distances  between  two 
poles  of  the  same  magnetic  mass  is  inversely  proportional  to 
the  squares  of  the  distances. 

(3)  The  force  exerted  at  a  given   distance  between  two 
poles  is  directly  proportional  to  the  product  of  the  magnetic 
masses  of  the  poles. 

(a)  Representing  the  force  acting  by  F,  the  magnetic  masses  by 
m  and  mf,  and  the  distance  between  the  poles  by  d,  and  measuring 


MAGNETISM.  463 

all  magnitudes  in  absolute  units,  we  may  summarize  the  last  two 

laws  thus :  — 

P_  mm' 

If,  in  this  equation,  we  make  m,  m',  and  d  each  equal  to  unity,  F  will 
also  be  equal  to  unity ;  i.e.,  a  unit  pole  exerts  unit  force  on  a  unit 
pole  at  unit  distance.  The  absolute  C.G.S.  unit  magnetic  pole  is, 
therefore,  a  pole  of  such  magnetic  mass  that,  when  placed  a  centi- 
meter distant  from  another  unit  pole,  the  force  between  them  shall 
be  one  dyne,  as  was  stated  in  §  367. 

372.  Magnetic  Potential  is  essentially  analogous  to  elec- 
trostatic potential.     At  any  point,  it  is  measured  by  the 
work  done  against  the  magnetic  forces  in  moving  a  unit 
magnetic  pole  from  an  infinite  distance  to  the  given  point. 
The  difference  of  magnetic  potential  between  two  points  is 
measured  by  the  amount  of  work  required  to  move  a  unit 
magnetic  pole  from  one  to  the  other.     If  this  work  is  one 
erg,  there  is  unit  difference  of  potential  between  the  two 
points.      See  §  338. 

Magnetization. 

Experiment  340.  —  Place  a  short  rod  of  soft  iron  in  a  paper  stirrup, 
and  suspend  it  by  a  thread  over  and  near  the  poles  of  a  strong  horse- 
shoe magnet  that  is  supported  in  a  vertical  plane.  Bring  first  one 
end  of  a  bar  magnet,  and  then  the  other  end,  near  one  end  of  the  soft 
iron  rod,  and  determine  whether  the  suspended  iron  is  a  magnet  or 
not.  If  it  is,  ascertain  which  of  its  poles  is  over  the  marked  pole  of 
the  horseshoe  magnet. 

Experiment  341.  —  Support  a  bar  magnet  in  a  horizontal  position 
6  or  7  cm.  above  the  table.  Bring  a  quantity  of  iron  tacks  to  one 
pole  so  that  as  many  as  possible  will  be  supported.  Place  a  similar 
magnet  on  the  table,  parallel  to  the  first  but  with  its  poles  in  reversed 
position.  Test  the  upper  magnet  for  increase  or  decrease  of  lifting 
power. 

373.  Magnetization.  — Any  magnetic  substance  is  mag- 
netized by  bringing  it  into   contact  with  a  magnet,   or 


464  SCHOOL  PHYSICS. 

simply  by  placing  it  in  a  magnetic  field.  In  the  latter 
case,  it  is  said  to  be  magnetized  by  induction.  If  the 
substance  is  paramagnetic,  its  magnetic  axis  will  coincide 
with  the  lines  of  force  of  the  field.  The  amount  of  magne- 
tization developed  depends  upon  the  nature  of  the  sub- 
stance and  the  strength  of  the  field. 

(a)  With  a  given  field,  iron  receives  the  greatest  amount  of  mag- 
netization, steel  coming  next.  As  the  magnetizing  force  increases, 
the  magnetization  produced  also  increases,  rapidly  at  first  but  more 
and  more  slowly.  When  the  magnetization  ceases  to  increase,  the 
substance  is  said  to  be  saturated;  the  saturation  point  is,  therefore, 
a  function  of  the  magnetizing  force. 

Theory  of  Magnetization. 

Experiment  342.  —  Heat  a  magnetized  needle  to  redness  and,  when 
it  has  cooled,  test  it  for  magnetism.  Put  a  magnetized  knitting- 
needle  into  active  vibration  (see  Fig.  149),  and  subsequently  test  it 
for  magnetism.  In  each  case,  the  magnetization  will  be  weakened 
or  destroyed. 

Experiment  343.  —  Magnetize  a  piece  of  watch-spring  about  10  cm. 
long,  and  ascertain  how  large  a  nail  it  will  support.  Bring  the  two 
ends  of  the  magnets  into  contact.  The  ring  thus  formed  manifests 
no  polarity,  thus  showing  the  equality  of  the  opposite  poles.  Break 
the  magnet  at  its  middle,  and  test  the  strength  of  magnetization  of 
the  two  new  poles  developed  at  the  point  of  fracture. 

Experiment  344.  —  Nearly  fill  a  slender  glass  tube  with  steel  filings, 
and  close  the  ends  of  the  tube  with  corks.  Draw  the  marked  pole  of 
a  strong  magnet  from  the  middle  of  the  tube  to  one  end,  and  the 
unmarked  pole  from  the  middle  to  the  other  end,  and  repeat  the 
stroking  several  times.  One  end  of  the  tube  will  attract  and  the  other 
will  repel  the  marked  pole  of  a  suspended  magnetic  needle ;  i.e.,  j;he 
filled  tube  has  become  a  magnet.  Thoroughly  shake  up  the  filings; 
the  tube  loses  its  magnetic  properties,  as  if  the  actions  of  the  many 
little  magnets  in  the  tube  were  neutralized  through  their  indiscrimi- 
nate arrangement. 


MAGNETISM.  465 

374.  Theory  of  Magnetic  Polarization. — When  a  magnet 
is  broken,  each  piece  becomes  a  magnet,  the  newly  developed 
poles  being  of  strength  nearly  equal  to  that  of  the  original 
poles.  The  subdivision  of  the  magnet  may  be  carried  on 
indefinitely,  and  with  the  same  results.  This  suggests 
that  the  magnetic  property  must  reside  in  the  smallest 
particle  capable  of  existing  by  itself,  i.e.,  the  molecule. 
It  is  easy  to  imagine  that  if  the  steel  particles  in  the 
shaken  tube  of  Experiment  344  could  be  restored  to  their 
former  positions,  the  tube  would  again  act  as  a  magnet. 
It  may  be  assumed  that  the  molecules  of  a  magnetic  sub- 
stance are  always  magnets;  that  the  substance  does  not 
exhibit  magnetic  properties  when  the  magnetic  axes  of  the 
molecules  are  turned  indifferently  in  every  direction;  and 
that  the  process  of  magnetization  consists  in  turning  the  mole- 
cules so  that  their  axes  point  in  the  same  direction.  When 
the  axes  of  all  the  molecules  have  thus  been  set  parallel, 
the  maximum  of  magnetization  has  been  secured. 

(a)  Magnetization  changes  the  length  but  not  the  volume  of  the 
bar  magnetized.  When  soft  iron  is  rapidly  magnetized  and  demag- 
netized, it  becomes  heated,  and  sometimes  a  clicking  sound  is  produced 
at  each  change. 

Magnetic  Properties  of  Electric  Currents. 

Experiment  345.  —  Repeat  Experiment  315,  and  test  the  accuracy 
of  the  following  rules :  — 

(1)  To  determine  the  direction  of  the  deflection  of  the  needle, 
hold  the  open  right  hand  over  or  under  the  conducting  wire,  but  so 
that  the  wire  is  between  the  hand  and  the  needle,  so  that  the  palm 
of  the  hand  is  toward  the  needle,  and  so  that  the  fingers  point  in  the 
direction  of  the  current ;    the  marked  end  of  the  needle  will  turn 
in  the  direction  of  the  extended  thumb. 

(2)  To  determine  the  direction  of  the  current,  hold  the  open  right 
hand  over  or  under  the  conducting  wire,  but  so  that  the  wire  is 


466 


SCHOOL   PHYSICS. 


between  the  hand  and  the  needle,  so  that  the  palm  of  the  hand 
is  toward  the  needle,  and  so  that  the  thumb  is  extended  in  the  direc- 
tion in  which  the  marked  end  of  the  needle  is  deflected ;  the  fingers 
will  point  in  the  direction  of  the  current. 

Experiment  346.  —  Dip  a  short  part  of  a  stout  copper  wire  that  is 
carrying  a  large  current  into  fine  iron  filings.  A  cluster  of  the  filings 
will  cling  to  the  wire. 

Note. —  If  you  cannot  obtain  an  electric-light  or  a  trolley-wire 
current  for  the  next  experiment,  connect  a  number  of  similar  cells  in 
parallel.  Make  the  external  circuit  of  very  heavy  wire,  and  have  the 
paper  in  place  around  the  wire,  and  the  dredge-box  ready.  Close  the 
circuit  and  perform  the  experiment  quickly. 

Experiment  347.  —  Around  a  vertical  conductor  carrying  a  heavy 
current,  place  a  piece  of  paper  cut  as  shown  in  Fig.  358,  and  sprinkle 
fine  iron  filings  on  the  paper.  Notice  that  the  iron  particles  arrange 
themselves  in  distinct  circular  whirls  around  the  wire,  as  shown  in 
Fig.  359.  Experimentally  establish  the  tangential  relation  between 
a  short  magnet  and  these  curves,  as  in  Experiment  335.  Hold  the 
closed  right  hand  so  that  the  extended  thumb  points  in  the  direction 
of  the  current  in 
the  wire ;  then  the 
fingers  will  indi- 
cate the  direction 
of  the  lines  of 
force  in  the  sur- 
rounding field. 
Bend  the  upper 
part  of  the  con- 
ducting wire,  and  FIQ 
pass  it  vertically  downward  through  the 
paper.  Sprinkle  iron  filings  as  before.  Notice  that  the  magnetic 
lines  of  force  around  the  two  parallel  parts  of  the  wire  circle  in 
opposite  directions,  clockwise  in  one  case,  and  counter-clockwise  in 
the  other.  If  the  conducting  wire  is  bent  into  the  form  shown 
in  Fig.  360,  the  lines  of  force  will  pass  around  the  wire  from  one  face 
of  the  loop  to  the  other,  and  in  the  direction  indicated  by  the  "rule  of 
thumb  "  just  given. 

Experiment  348.  —  Bend  a  piece  of  stout  copper  wire  into  the  form 
shown  in  Fig.  360.  Suspend  it  at  its  highest  point  by  a  long  thread 


FIG.  358. 


MAGNETISM. 


467 


and  so  that  its  free  ends  just  dip  into  mercury  contained  in  sepa- 
rate, shallow  dishes.  Put  the  apparatus 
into  the  circuit  of  a  strong  electric  cur- 
rent, making  connections  with  the  mer- 
cury cups.  Bring  a  bar  magnet  near 
either  face  of  the  circular  conductor. 
The  loop  will  turn  upon  its  vertical  axis, 
seeking  a  position  at  right  angles  to 
the  magnet,  and  acting  as  if  it  was  a  disk 
magnet  with  poles  at  its  faces. 


FIG.  360. 


Experiment  349.  —  Coil  some  No.  12 

copper  wire  through  holes  in  a  board, 

as  shown  in  Fig.  361,  and  pass  a  strong 

current  through  it.  Sprinkle  iron  filings  as  before  and  note  the 

effect.  Such  a  coil  of  conducting 
wire,  wound  so  as  to  afford  a  num- 
ber of  equal  and  parallel  circular 
electric  circuits  arranged  upon  a 
common  axis,  is  called  a  solenoid. 

Experiment  350.  —  Wind ,  the 
middle  part  of  about  3  meters  of 
Xo.  20  insulated  copper  wire  around 
a  rod  about  1.5  cm.  in  diameter, 
forming  thus  a  solenoid  about 
10  cm.  long.  Bring  the  ends  of  the 
wire  along  the  axis  of  the  sole- 
noid, and  bend  them  at  right  angles 
near  the  middle.  Solder  small 
plates  of  sheet  copper  and  amalga- 
mated sheet  zinc  to  the  ends  of  the  wire.  Support  the  solenoid  and 

plates  by  a  large  flat  cork  on  the  surface  of 

dilute  sulphuric  acid,  as  shown  in  Fig.  362. 

The  floating  cell  will  take  position  so  that  the 

axis  of  the  solenoid  extends  north  and  south. 

Test  the  ends  of  the  solenoid  for  polarity, 

using  a  bar  magnet  for  that  purpose. 


FIG.  3(31. 


Experiment  351.  —  Repeat  Experiment  315, 


c  z 
FIG.  362. 


468 


SCHOOL  PHYSICS. 


using  the  floating  cell  of  Experiment  350  instead  of  the  compass, 
needle. 

Experiment  352.  —  Prepare  a  second  solenoid  similar  to  that  de- 
scribed in  Experiment  350,  omitting  the 
plates.  Put  it  into  an  electric  circuit,  and 
use  it  as  you  did  the  bar  magnet  in  Ex- 
periment 350. 


375.    The  Magnetic  Character  of 
an  Electric  Current  has  been  shown 

FIG.  363.  .  -,         -,    n  P      , 

by  the  deflection  of   the  magnetic 

needle,  by  the  production  of  phantom  curves,  and  by 
other  experiments.  The  passage  of  an  electric  current 
through  a  solenoid  gives  it  many  of  the  properties  of  a 
cylindrical  bar  magnet. 

(a)  The  polarity  of  the  solenoidal  magnet  may  be  determined  by 
holding  it  in  the  right  hand  so  that  the  fingers  point  in  the  direction 
of  the  current;   then  the  extended 
thumb  will  point  toward  the  marked 
or  north-seeking  pole  of  the  magnet. 
The  lines   of   force    flow   from  the 
marked  to  the  unmarked  pole  out- 
side the  solenoid,  and  in  the  oppo-  -jiPL     N 
site   direction   inside    the   solenoid. 
Looking  at  one  end   of  a  solenoid 
so   that  the  current  circles  around 
clockwise,  you  may  imagine  that  the 
enclosed  lines  of  force  go  forward, 
just  as  the  right-hand  turning  of  a 
corkscrew  is  related  to  its  forward 
motion.     .Two  solenoids  freely  sus- 
pended act  toward  each  other  as  did 
the  suspended  magnets  of  Experi-                        pIG  364< 
ment  339. 

376.    Magnetomotive   Force.  —  The   influence  to  which 
these  magnetic  lines  of  force  are  due  is  called  magneto- 


MAGNETISM.  469 

motive  force  (M.M.F.).  The  magnetomotive  force  of  a 
magnetic  circuit  is  directly  proportional  to  the  number 
of  amperes  in  the  electric  circuit  surrounding  it,  and  to 
the  number  of  turns  that  the  electric  circuit  makes  around 
the  magnetic  circuit ;  i.e.,  the  magnetomotive  force  is  pro- 
portional to  the  ampere-turns.  The  unit  of  magnetomotive 
force  is  called  a  gilbert,  and  corresponds  to  0.7958 
ampere-turns. 

Experiment  353.  —  Place  a  strip  of  sheet  iron  in  the  solenoid  of 
Experiment  350,  as  shown  in  Fig. 
365,  and  repeat  that  experiment. 
Notice  that  most  of  the  lines  of  force 
are  gathered  into  the  iron  and  issue 
from  its  ends.  Notice  that  the  lines 
curve  outward  and  tend  to  return. 
forming  closed  loops  or  complete 
magnetic  circuits.  Change  the  iron 
from  the  inside  of  the  solenoid  to  the 
outside,  and  repeat  the  experiment. 
Notice  that  the  iron  again  gathers  in 
the  lines  of  force  as  if  it  offered  an 
easier  path  for  them. 

377.  Permeability.  —  Some  substances  are  capable  of 
receiving  more  lines  of  force  than  others  with  the  same 
magnetomotive  force.  This  relative  capacity  is  called 
permeability,  which  may  be  denned  as  the  ratio  between 
the  number  of  lines  of  force  that  pass  through  a  given 
area  of  the  substance  and  the  number  of  lines  of  force 
that  pass  through  a  like  area  of  the  inducing  field  alone. 
It  is  a  sort  of  magnetic  conductivity. 

(a)  The  permeability  of  paramagnetic  substances  is  greater  than 
unity;  that  of  diamagnetic  substances  is  less  than  unity.  Bismuth 
has  the  lowest  permeability  of  any  known  substance.  When  a 


470  SCHOOL  PHYSICS. 

paramagnetic  substance  is  placed  in  a  uniform  magnetic  field,  its 
permeability  being  greater  than  that  of  the  field,  an  increased  number 
of  lines  of  force  are  crowded  into  it,  as  shown  in  Fig.  366.  When  a 

diamagnetic  substance  is  placed 
in  such  a  field,  its  permeability 
being  less  than  that  of  the  field, 
the  number  of  lines  that  pass 
through  it  is  diminished,  as  shown 
in  Fig.  367. 

(b)  If  a  small  compass  is  put 

P,       „,.[.  into  a  closed  bottle,   an  outside 

magnet  will  affect  it,  but  if  it  is 
put  into  a  hollow  iron    ball,  an  outside   magnet  will  not  affect  it. 
Soft    iron    acts    as    a   magnetic 
screen  (§  370)  because  of  its  high 
permeability.    Watches  are  some- 
times   protected   from  magnetic 
influence  by  soft  iron  shields  in 
the  shape  of  inside  cases. 


378.  Reluctance  and  Re- 

FIG.  .367. 

luctivity.  —  Like      electric 

currents,  magnetic  lines  of  force  flow  in  the  greatest 
quantity  through  paths  of  least  resistance.  Magnetic 
resistance  is  called  reluctance,  and  its  unit  is  the  oersted. 
Specific  magnetic  resistance  (specific  reluctance)  is 
called  reluctivity.  Reluctivity  is  the  reciprocal  of  per- 
meability. 

379.  The  Analogue  of  Ohm's  Law.  — In  §  361,  we  have  a 
formula  that  shows  the  mathematical  relations  between 
amperes,  volts,  and  ohms.      The  corresponding  relations 
for  magnetic  units  is  expressed  by  the  equation,  — 

weber*  =  &*«* .  (1) 

oersteds 


MAGNETISM.  471 

From  this  we  may  derive  the  other  two,  — 

gilberts  =  webers  x  oersteds,  and  (2) 


webers 
These  formulas  are  much  used  in  magnetic  calculation. 

Coercive  Force. 

Experiment  354.  —  Prepare  three  small  bars  of  the  same  size,  one 
of  soft  iron,  one  of  soft  steel,  and  one  of  hardened  steel.  Bring  one 
end  of  a  good  bar  magnet  into  contact  with  one  end  of  the  iron  bar, 
and  dip  the  other  end  of  the  iron  bar  into  iron  filings.  Lift  the  mag- 
net and  the  iron  bar  without  breaking  the  contact  between  them. 
Xotice  the  quantity  of  filings  lifted  by  the  iron.  Break  the  contact, 
and  notice  the  quantity  of  filings  dropped  by  the  iron.  Repeat  the 
test  with  the  other  two  bars  in  succession.  It  will  be  found  that  the 
iron  will  lift  the  most  and  the  hardened  steel  the  least,  but  that, 
when  the  contact  is  broken,  the  hardened  steel  holds  the  most  and 
the  iron  the  least. 

Experiment  355.  —  With  the  end  of  a  good  bar  magnet,  write  your 
name  upon  the  blade  of  a  hand  saw.  The  invisible  characters  may 
be  made  visible  by  sifting  fine  iron  filings  upon  the  blade. 

Experiment  356.  —  Lay  a  thin  piece  of  well-hardened  steel  (it 
may  be  cut  from  a  saw-blade)  in  the  solenoid,  and  repeat  Experiment 
353.  After  the  current  has  been  interrupted,  jar  the  solenoid,  and 
notice  that  some  of  the  filings  are  still  held  in  their  positions.  The 
hard  steel  has  become  a  permanent  magnet. 

380.  Coercive  Force  and  Remanance.  —  The  persisting 
magnetomotive  force  shown  by  tne  steel  is  due  to  what 
is  called  the  coercive  force  of  the  steel,  which  acts  as  a  sort 
of  magnetic  inertia,  resisting  magnetization  at  the  outset 
and  tending  to  retain  it  afterward.  The  number  of  lines 
of  force  per  square  centimeter  in  the  body  of  the  steel  is 
called  its  remanance. 


472 


SCHOOL  PHYSICS. 


(a)  Coercive  force  is  measured  in  gilberts ;  remanance,  in  gausses. 

Experiment  357.  —  Make  a  helix  about  15  era.  long  by  neatly 
winding  three  layers  of  No.  18  insulated  copper  wire  upon  a  rod  about 
2  cm.  in  diameter.  Remove  the  rod,  pass  a  few  threads  through  the 
opening  of  the  helix,  and  tie  them  on  the  outside  so  as  to  hold  the 
turns  of  wire  in  place.  Put  the  helix  into  the  circuit  of  a  voltaic  cell, 
and  bring  it  near  a  magnetic  needle.  The  deflection  of  the  needle 
shows  the  magnetic  power  of  the  helix.  Nearly  fill  the  opening  in 
the  helix  with  straight  pieces  of  soft  iron  wire,  and  again  test  its 
magnetic  power.  The  deflection  of  the  needle  will  be  much  greater 
than  before. 


381. 

electric 


An  Electromagnet  is  a  bar  of  iron  magnetized  by  an 
current,  substantially  as  just  shown.  When  the 
current  was  passed  through  the 
helix  used  in  Experiment  357,  some 
of  the  lines  of  force  leaked  out  at 
the  sides,  as  indicated  by  Fig.  368, 
and  few  of  them  extended  from 
end  to  end.  The  soft  iron  core, 
by  reason  of  its  high  permeability, 
diminished  this  leakage  of  lines  of 
force,  and  greatly  increased  their 
number,  as  shown  in  Fig.  369. 


(a)  Since  the  lines  of  force  are  perpen- 
dicular to  the  direction  of  the  current,  the 
FIG.  368.      i1011  core  *s  to  be  placed  at  right  angles  to       FIG.  369. 

the  wire ;   the  ^effect  is    increased  by  in- 
creasing the  number  of  turns  of  the  wire.     The  direction  of  polarity 
in  the  core  depends  only  upon  the  direction  of  the  current  in  the 
helix,  and  may  be  determined  by  the  thumb  or  the  corkscrew  rule 
already  given. 

(6)  When  an  electromagnet  is  U-snaPed>  tne  co^s  around  the  two 
ends  of  the  bent  iron  core  are  so  wound  that  if  the  coil  should  be 
straightened  either  coil  would  appear  as  a  continuation  of  the  other, 


FIG.  370. 


UNIVERSITY  OF  CALIFORNIA 

DEPARTMENT  OF  PHYSJCS 

MAGNETISM.  473 

i.e.,  the  current  would  circle  around  the  core  in  the  same  direction  in 
the  two  coils.     Such  magnets  are  often  made  by  connecting  an  end 
of  the  core  of  one  spool-shaped  magnet, 
by  a  straight   soft   iron   bar  called   a 
yoke,  to  one  end  of  the  core  of  a  sim- 
ilar magnet,  a  screw  passing  through 
the  bar  into  an  end  of   each  straight 
core.     The  two   spools   are   then   con- 
nected as  above  indicated. 

(c)  To  produce  the  best  effect,  the 
resistance  of  the  electromagnet  should 
be  equal  to  that  of  the  rest  of  the  cir- 
cuit.   If  several  electromagnets  are  used 
on  the  same  circuit,  the  sum  of  their 

resistances  should  equal  the  resistance  of  the  rest  of  the  circuit. 

(d)  If  the  iron  of  the  magnet  core  is  of  commercial  quality,  it  is 
not  wholly  demagnetized  when  the  current  is  interrupted.     The  mag- 
netization thus  retained  after  withdrawal  from  a  magnetic  field  is 
called  residual  magnetism. 

382.  Ampere's  Theory  of  Magnetism. — As  an  electric 
current  is  surrounded  by  a  whirl  of  lines  of  magnetic 
force,  so  we  may  conceive  a  magnetic  line  of  force  as 
surrounded  by  an  electrical  current-whirl.  This  would 
imply,  as  Ampere  long  ago  suggested,  that  magnetism  is 
simply  a  vortical  electric  current,  and  that  a  magnetic 
field  is  something  like  a  whirlpool  of  electricity.  Fig.  371 
represents  a  vertical  conductor  carrying  an 
electric  current,  and  surrounded  by  a  mag- 
netic line  of  force,  which  is  in  turn  sur- 
rounded by  electric  whirls  ;  the  magnetic  line 
of  force  is  an  electric  vortex-ring.  It  is  not 
difficult  to  conceive  the  vortex-ring  as  made 
up  of  ether  whirls.  As  the  phenomena  of 
magnetism  belong  to  the  molecules,  these  electrical  whirls 
must  be  rotations  perpendicular  to  the  magnetic  axes  of 


FIG.  371. 


474  SCHOOL  PHYSICS. 

the  molecules.  Ampere's  theory  supposes  that  electric 
currents  circle  round  the  molecules  of  a  magnetic  sub- 
stance, thereby  polarizing  them,  and  that  when  all  these 
magnetic  axes  face  in  the  same  direction  the  substance  is 
magnetically  saturated. 

(a)  The  great  importance  of  the  relation  between  magnetic  lines 
of  force  and  electric  currents  will  appear  more  plainly  in  the  following 
section. 

Terrestrial  Magnetism. 

Experiment  358. — Place  a  small  dipping-needle  over  the  marked 
end  of  a  long,  horizontal  bar  magnet,  and  move  it  slowly  toward  the 
other  end  of  the  bar,  observing  the  changes  in  the  position  of  the 
dipping-needle.  Similar  changes  would  be  observed  if  you  could 
carry  the  dipping-needle  from  far  southern  to  far  northern  latitudes. 

Experiment  359.  —  Take  a  bar  of  very  soft  iron  about  75  cm.  long, 
and  make  sure  by  trial  that  its  ends  will  not  attract  bits  of  soft  iron. 
Then  hold  the  bar  in  a  meridian  plane,  and  with  its  north  end 
depressed  below  the  horizon  a  number  of  degrees  approximately 
corresponding  to  the  latitude  of  the  place  of  the  experiment,  i.e., 
give  it  the  position  of  a  dipping-needle.  Tap  the  rod  on  its  end  with 
a  mallet  or  wooden  block,  and  test  it  for  magnetic  polarity. 

383.  Terrestrial  Magnetism.  —  A  magnetic  field  is  recog- 
nized by  the  fact  that  it  gives  a  definite  direction  to  a 
magnet  freely  suspended  in  it.  The  directive  tendency 
of  the  compass,  and  other  phenomena,  show  that  the  earth 
is  surrounded  by  such  a  field.  In  fact,  these  phenomena 
are  such  as  might  be  expected  if  we  knew  that  a  bar 
magnet  four  or  five  thousand  miles  long  extended  nearly 
north  and  south  through  the  earth's  center.  This  terres- 
trial magnetism  is  explained  as  being  due  to  equatorial 
electric  currents  produced  by  the  action  of  the  sun,  and 
modified  by  the  motion  of  the  earth. 


MAGNETISM. 


475 


(a)  The  angle  that  the  axis  of  a  dipping-needle  makes  with  a 
horizontal  plane  is  called  the  inclination  or  dip  of  the  needle.  The  dip 
is  90°  at  the  magnetic  poles  of  the  earth,  and  0°  at  the  magnetic 
equator,  and,  at  any  given  place,  does  not  differ  greatly  from  the 
latitude.  Lines  passing  through  points  on  the  earth's  surface  where 
the  inclination  has  the  same  value  are  called  isoclinic  lines.  The 
inclination  of  the  needle  is  subject  at  most  places  to  secular,  annual, 
and  diurnal  changes. 

(6)  The  magnetic  poles  of  the  earth  do  not  coincide  with  its  geo- 
graphical poles  and,  consequently,  in  some  places,  the  magnetic  needle 
does  not  point  to  the  geographical  north.  The  angle  that  the  axis  of 
a  compass-needle  makes  with  the  geographical  meridian  at  any  place 
is  called  the  declination  or  variation  of  the  needle  at  that  place.  When 
the  marked  end  of  the  needle  lies  east  of  the  meridian,  the  variation 
is  easterly,  and  vice  versa.  Lines  drawn  through  places  on  the  earth 
where  the  declination  is  the 
same  are  called  isogonic  lines,  as 
is  shown  in  Fig.  372.  The  par- 
ticular isogonic  line  for  which 
the  declination  is  zero  is  called 
an  agone  or  an  agonic  line. 
These  lines  are  very  irregular, 
being  apparently  affected  by 
local  conditions.  The  Ameri- 
can agone,  in  1890,  entered  the 
United  States  near  Charleston^ 
passed  through  the  mountains 
of  North  Carolina  and  West 
Virginia,  and  near  Columbus, 
Toledo,  and  Ann  Arbor,  and  is  FIG.  372. 

slowly  moving  westward.     The 

declination  of  the  needle  is  subject  to  periodic  changes,  secular, 
annual,  and  diurnal,  and  to  irregular  variations  or  perturbations. 
The  mariner  or  the  surveyor  must  recognize  not  only  the  declination 
of  his  needle  but  also  the  changes  in  its  declination. 

(c)  The  magnetic  intensity  of  the  earth  is  also  an  element  that 
varies  from  point  to  point  at  the  same  time,  and  from  time  to  time 
at  the  same  place.  Lines  drawn  through  places  on  the  earth  where 
the  force  of  terrestrial  magnetism  is  the  same  are  called  isodynamic 
lines. 


476  SCHOOL  PHYSICS. 

(d)  The  determination  of  these  three  magnetic  elements  is  the 
object  of  governmental  magnetic  surveys. 

(«)  The  observed  coincidences  between  magnetic  storms,  i.e.,  sud- 
den disturbances  of  the  earth's  magnetism,  and  solar  storms  indicate 
a  connection,  the  nature  of  which  is  not  yet  well  understood. 

CLASSROOM  EXERCISES. 

1.  What  part  of  a  magnet  might  properly  be  designated  by  the 
term  equator  ? 

2.  Explain  the   increase  of  lifting  power  manifested  in  Experi- 
ment 357. 

3.  How  can  the  intensity  of  different  parts  of  a  magnetic  field  be 
roughly  estimated  from  the  behavior  of  a  magnetic  needle  ? 

4.  Show  that  the  influence  of  the  earth's  magnetism  upon  a  mag- 
netic needle  is  merely  directive. 

5.  If  a  wire  coil  of  220  turns  carries  a  3-ampere  current,  what  is  its 
magnetomotive  force?  Ans.  829  +  gilberts. 

6.  A  rectangular  bar  of  steel  1x3  cm.  and  30  cm.  long,  is  bent  into 
a  circle,  and  upon  it  is  wound  40  turns  of  wire.      A  o-ampere  current 
is  passed  through  the  wire,    (a)  Determine  the  M.M.F.    (6)  Assume 
the  reluctance  to  be  0.00593  oersteds,  and  divide  the  M.M.F.  by  the 
reluctance  to  determine  the  flux  of  force  in  webers.     (c)  Determine 
the  intensity  of  flux  in  gausses,     (d)  Assume  the  permeability  to  be 
1,684  and  determine  the  reluctivity,     (e)  Divide  the  M.M.F.  by  the 
length  of  the  bar  to  determine  the  magnetizing  force  in  gausses. 

LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  collection  of  bar  magnets ;  a  hack-saw 
blade ;  several  sheets  of  paper  about  50  cm.  square ;  a  compass  with  a 
needle  2  or  3  cm.  long. 

1.  By  observations  of  the  North  Star  or  in  any  other  convenient 
way,  mark  a  true  north  and  south  line  on  the  laboratory  table.     Place 
a  magnetic  needle  in  this  line,  and  determine  the  direction  and  mag- 
nitude of  the  declination. 

2.  Float  a  magnet  on  water  as  shown  in  Fig.  350.    The  float  should 
be  the  lightest  that  will  carry  the  load  with  safety,  and  the  body  of 
water  should  be  so  large  that  surface  tension  will  not  urge  the  float 
toward  the  side  of  the  vessel.     When  the  magnet  is  at  rest  near  the 


MAGNETISM.  477 

middle  of  the  liquid  surface,  determine  the  tendency  of  the  magnet  to 
drift  toward  the  north  or  south.  Repeat  the  experiment  with  a 
variety  of  magnets,  and  try  to  find  one  that  always  floats  in  one 
direction,  i.e.,  one  in  which  the  marked  pole  is  stronger  or  weaker 
than  the  other.  If  you  cannot  find  such  a  magnet,  strongly  magnetize 
the  blade  of  an  old  hack-saw,  and  test  it  on  the  float.  If  you  have 
not  yet  found  that  for  which  you  seek,  break  the  blade  in  the  middle, 
and  test  each  half.  If  necessary  to  the  success  of  your  search,  break 
one  of  the  halves  in  two,  and  repeat  the  tests.  Make  very  careful 
notes  of  any  magnet  that  you  find  to  have  more  magnetism  of  one 
kind  than  of  the  other. 

3.  Fasten  a  large  sheet  of  paper  upon  the  table-top.     Place  a  bar 
magnet  about  20  cm.  long  and  1  sq.  cm.  in  cross-section  upon  the 
middle  of  the  paper  with  its  marked  end  pointing  toward  the  north. 
Place  a  small  compass  on  the  paper  at  the  northeast  corner  of  the 
magnet,  move  it  away  from  the  magnet  in  the  direction  in  which  the 
marked  end  of  the  needle  points,  tracing  upon  the  paper  the  path  of 
the  middle  point  of  the  compass,  and  indicating  by  arrow-heads  upon 
the  line  thus  traced  the  direction  in  which  the  compass  is  moved. 
Continue  the  movement  of  the  compass,  continually  changing  the 
direction  of  the  motion  of  the  compass  as  indicated  by  the  direction 
in  which  the  marked  end  of  the  needle  points,  until  the  traced  path 
reaches  the  edge  of  the  paper  or  returns  to  the  magnet.      Repeat  the 
work,  starting  near  the  same  corner  but  1  cm.  nearer  the  middle  of 
the  magnet.     Taking  the  successive  starting  points  nearer  and  nearer 
the  middle  of  the  magnet,  continue  to  draw  such  lines  until  you  come 
within  about  3  cm.  of  the  middle  of  the  bar.     Similarly,  trace  an 
equal  number  of  lines  on  the  other  side  of  the  magnet.     The  curves 
may  be  traced  in  an  "  off-hand  "  way,  their  general  character  being  of 
more  importance  than  exact  details.     Trace  the  outline  of  the  mag- 
net on  the  paper,  and  indicate  its  polarity. 

4.  Place  the  magnet  used  in  Exercise  3  upon  a  clean  sheet  of  paper, 
and  with  its  marked  end  pointing  toward  the  south.     Trace  lines  as 
indicated  in  that  exercise. 

5.  Place  two  similar  bar  magnets  on  a  clean  sheet  of  paper,  parallel 
to  each  other,  about  15  cm.  apart,  and  with  their  marked  ends  point- 
ing toward  the  north.     In  manner  similar  to  that  prescribed  for 
Exercise  3,  trace  the  lines  of  force,  including  several  lines  between  the 
two  magnets.     Compare  this  diagram  with  those  drawn  in  Exercises 
3    and   4,    specify    their   characteristic  features,   and  explain    their 
significance. 


478  SCHOOL  PHYSICS. 

6.  Map  a  magnetic  field  as  in  Experiment  335.  Carefully  remove 
the  rnagnet  and  wooden  strips.  Over  the  filings,  carefully  place  a  sheet 
of  printing-paper  that  has  been  wet  with  a  solution  of  tannin.  Over 
this,  place  a  sheet  of  heavy  blotting-paper.  Place  a  board  on  the 
blotting-paper  and  a  weight  on  the  board.  When  the  printing-paper 
is  removed,  some  of  the  iron  filings  will  adhere  to  it.  When  the 
paper  is  dry,  brush  off  these  filings.  The  ink-like  markings  on  the 
paper  make  a  permanent  copy  of  the  map. 


II.    ELECTRIC    GENERATORS,  ELECTROMAGNETIC 
INDUCTION,  ETC. 

384.  Introductory.  —  We  have  seen  that  when  two  bodies 
at  different  electric  potentials  are  connected  by  a  conductor, 
an  electric  current  transfers  along  the  conductor  the  state 
of  strain  that  constitutes  electrification.      If  that  strain  is 
reproduced  as  fast  as  it  is  relieved,  the  difference  of  poten- 
tial will  be  constant,  and  the  current  will  be  continuous 
and  uniform.     The  devices  considered  in  the  preceding 
section  are  incapable  of  producing  a  current  adequate  to 
the  demands  of  the  age  in  which  we  live.     It  is  the  pur- 
pose of  this  section  to  indicate  how  such   currents   are 
produced. 

385.  Voltaic  Cells  are  among   the   most  common  and 
important  of  "electric  generators,"  and  have  been  devised 
in  great  variety.      Some  of  them  are  dry,  some  have  one 
liquid,  and   others   have   two.      Some  are    constant   and 
strong  while  they  last,  but  require  frequent  renewals ; 
others  are  effective  for  short  periods  only,  and  require 
time  for  their  own  recovery.     Each  has  its  advantages 


ELECTRIC    GENERATORS,    ETC.  479 

and  its  disadvantages,  so  that  one  is  the  better  for  one  pur- 
pose, and  another  for  another. 

(a)  When  commercial  zinc  is  used  as  one  of  the  plates  of  a  cell, 
the  chemical  action  shown  in  Experiment  312,  and  known  as  local 
action,  contributes  nothing  to  the  current.  It  is  probably  due  to  the 
presence  of  particles  of  carbon,  iron,  etc.,  in  the  zinc.  The  zinc  and 
these  foreign  particles  in  the  zinc  act  as  the  plates  of  minute  voltaic 
cells,  the  currents  flowing  in  short  circuits  from  the  zinc  through  the 
liquid  to  the  foreign  particles,  and  thence  back  to  the  zinc.  This  local 
action  is  prevented  by  using  pure  zinc,  or  by  amalgamating  commercial 
zinc  as  in  Experiment  313. 

(6)  The  polarization  of  the  cell,  i.e.,  the  accumulation  of  the  hydro- 
gen film  on  the  negative  plate,  interferes  with  the  action  of  the  cell 
and  diminishes  the  available  current  by  increasing  the  resistance  of 
the  circuit,  and  by  setting  up  a  counter  electromotive  force  that  may 
reduce,  stop  or  even  reverse  the  flow  of  the  current.  The  various 
devices  for  removing  the  hydrogen,  or  for  preventing  its  accumulation, 
constitute  the  most  essential  differences  between  the  diiferent  forms 
of  cells.  These  devices  may  be  classified  as  physical  (e.g.,  the  mechan- 
ical agitation  of  the  liquid,  or  the  roughening  of  the  plate  to  lessen  the 
adhesion  of  the  gas),  and  chemical  (e.g.,  the  use  of  some  agent,  like 
nitric  or  chromic  acid  or  manganese  dioxide,  for  the  oxidation  of  the 
hydrogen  before  it  reaches  the  negative  plate). 

Note.  —  The  oxidation  of  hydrogen  yields  water. 

(c)  A  few  forms  of  cells  are  mentioned,  although  it  is  impossible  to 
give  descriptions  of  all  or  many.  For  such  descriptions,  the  pupil  is 
referred  to  some  technical  work  on  the  subject. 

(1)  The  Smee  cell  consists  of  a  silver  or  a  lead  plate  suspended 
between  two  zinc  plates  immersed  in  dilute  sulphuric  acid.     Polariza- 
tion is  partly  prevented  by  giving  the  negative  plate  a  rough  coat  of 
finely  divided  platinum. 

(2)  The  potassium  dichromate  cell  (see  Experiment  316)  consists 
of    zinc   and   carbon   plates   immersed  in   a  solution   of  potassium 
dichromate  in  dilute  sulphuric  acid.     The  action  of  the  sulphuric  acid 
on  the  dichromate  liberates  chromic  acid  which  oxidizes  the  hydro- 
gen, and  thus  prevents  polarization.     This  cell  is  very  convenient  for 
quick  use,  and  valuable  for   "all-around"  work.     It   is   sometimes 
called  the  Grenet  cell.     A  similar  cell  that  employs  sodium  dichromate 


480  SCHOOL  PHYSICS. 

instead  of  potassium  dichromate  is  more  enduring  in  its  action.  A 
solution  of  chromic  acid  is  much  used  and  is  more  economical  than 
either. 

(3)  In  the  Grove  cell,  a  cylindrical  plate  of  zinc  is  immersed  in 
dilute  sulphuric  acid,  and  carries  a  porous  cup  that  contains  strong 
nitric  acid  in  which  a  platinum  strip  is  immersed.     The  hydrogen 
evolved  at  the  zinc  plate  is  oxidized  by  the  nitric  acid. 

(4)  The  Bunsen  cell  differs  from  the  Grove  in  a  substitution  of 
carbon  for  platinum,  and  in  the  larger  size  of  the  plates.     Like  the 
Grove  cell,  it  is  little  used,  the  fumes  that  come  from  the  nitric  acid 
being  choking  and  corrosive. 

(5)  In  the  Leclanche  cell,  a  zinc  rod  is  immersed  in  a  saturated 
solution  of  ammonium  chloride  (sal-ammoniac).     In  this  solution  is 
also  a  porous  cup  that  contains  a  bar  of  carbon  tightly  packed  in  a 
mixture  of  granular  carbon  and  manganese  dioxide.     The  hydrogen 
evolved  is  oxidized  by  the  dioxide,  but  so  slowly  that  the  cell  must  be 
given  frequent  intervals  of  rest  to  recover  from  polarization.     This 
cell  is  much  used  for  working  telephones,  electric  bells,  etc.,  i.e.,  on 
circuits  that  are  open  most  of  the  time. 

(6)  The  Daniell  cell  consists  of  a  zinc  plate  immersed  in  dilute  sul- 
phuric acid  contained  in  a  porous  vessel  outside  of  which  is  a  perfo- 
rated copper  plate  surrounded  by  a  solution  of  copper  sulphate.    The 
hydrogen  is  taken  up  by  the  sulphate  before  it  reaches  the  copper 
plate.     Polarization  being  wholly  prevented,  this  cell  is  one  of  the 
most  constant  known. 

(7)  The  gravity  cell  is  a  modification  of  the  Daniell.     The  liquids 
are  kept  separate  by  their  different  densities,  thus  dispensing  with 
the  porous  cup.    It  is  commonly  used  on  closed  circuits.     This  is  the 
form  of  cell  most  used  for  telegraphic  purposes  in  the  United  States. 

(rf)  Every  cell  has  an  internal  resistance  that  consists  chiefly  of  the 
resistance  of  the  liquid  or  liquids  used.  The  voltage  of  the  cell  is 
largely  taken  up  in  overcoming  this  internal  resistance,  thus  greatly 
lessening  the  energy  available  at  the  electrodes.  If  R  is  the  resistance 
of  the  circuit  outside  the  cell,  and  r  is  the  resistance  of  the  cell  itself, 
then  Ohm's  law  becomes 

c— £-. 

r+R 

Refer  to  Fig.  335,  and  notice  that  the  liquid  prism  between  the  plates 
is  part  of  the  circuit ;  that  when  the  plates  are  separated,  the  length 
of  the  liquid  conductor,  and  the  internal  resistance  of  the  cell,  are  in- 


ELECTRIC   GENERATORS,   ETC. 


481 


creased  (see  §  352)  ;  that  when  one  of  the  plates  is  lifted  partly  from 
the  liquid,  the  area  of  cross-section  is  reduced,  and  the  resistance 
increased. 

Experiment  360.  —  Upon  each  end  of  a  4-inch  piece  of  soft,  round 
iron-rod  1  inch  in  diameter,  drive  a  vulcanite  or  hard-wood  collar 
about  1£  inches  in  diameter. 
Upon  the  spool  thus  formed, 
wind  about  6  feet  of  No.  8  in- 
sulated copper  wire,  being  care- 
ful first  to  insulate  the  iron  core 
with  paper.  Fasten  a  rectan- 
gular piece  of  soft  iron,  a,  to 
a  piece  of  whalebone  and  sup- 
port it,  as  shown  in  Fig.  373, 
over  M,  the  electromagnet  just 

described.  Place  M  in  the  circuit  of  a  battery  of  six  or  more  similar 
cells  joined  in  series.  The  whalebone  magnetoscope  will  enable  you 
to  make  a  rough  estimate  of  the  pull  of  the  electromagnet. 

Experiment  361.  —  Connect  the  cells  of  the  battery  in  parallel,  and 
repeat  Experiment  360. 

Experiment  362.  —  Make  an  electromagnet  similar  to  that  of  Experi- 
ment 360,  but  using  about  250  feet  of  No.  24  insulated  copper  wire, 
and  with  it,  repeat  Experiments  360  and  361. 

Experiment  363.  —  Connect  the  terminals  of  the  high  resistance 
galvanoscope  described  in  Experiment  321  to  the  poles  of  a  single 
cell,  and  record  the  deflection  of  the  needle.  Next,  put  the  galvano- 
scope in  circuit  with  a  battery  of  six  similar  cells  joined  in  parallel, 
and  record  the  deflection  of  the  needle.  Then  put  the  galvanoscope  in 
circuit  with  a  battery  of  the  same  cells  joined  in  series,  and  record  the 
deflection  of  the  needle.  From  the  records,  determine  which  method 
of  joining  cells  is  most  effective  with  a  high  external  resistance. 

386.  Advantages  of  Grouping  in  Parallel.  —  Some  of  the 
foregoing  experiments  indicate  what  is  a  general  truth, 
that,  \vhen  the  external  resistance  is  small,  the  grouping 
of  electric  generators  in  parallel  will  give  a  greater  cur- 
rent than  will  a  series  grouping  of  the  same  generators. 
31 


482  SCHOOL   PHYSICS, 

(a)  With  such  a  grouping,  the  available  difference  of  potential 
between  the  terminals  of  the  system  is  not  increased,  but  the  internal 
resistance  is  diminished  (see  §  448).  For  instance,  with  n  cells  thus 
grouped,  we  have  j? 

C= • 


It  is  evident  that  the  less  the  value  of  R,  the  greater  will  be  the  effect 
of  n  in  increasing  the  value  of  C. 

387.  Advantages  of  Grouping  in  Series.  —  Our  experi- 
ments also  indicate  that  when  the  external  resistance  is 
great,  the  grouping  of  electric  generators  in  series  will 
give  a  greater  current  than  will  a  parallel  grouping  of  the 
same  generators. 

(«)  With  such  a  grouping,  the  voltages  of  the  several  generators 
are  added  together  for  the  total  available  difference  of  potential,  and 
the  internal  resistances  are  added  together  for  the  total  internal  resist- 
ance of  the  system.  With  n  cells  thus  grouped,  we  have 

C=     nE     • 
nr  +  R 

It  is  evident  that  when  R  is  small,  the  effect  of  n  upon  the  value  of  C 
must  also  be  small,  but  that  when  R  is  large,  the  effect  of  multiplying 
r  is  more  than  counterbalanced  by  the  corresponding  multiplication 
of  E. 

(b)  Having  a  given  number  of  similar  cells  and  a  certain  known 
external  resistance,  the  maximum  current  may  be  obtained  by  joining 
the  cells  in  such  a  way  as  to  make  the  resistance  of  the  battery  as 
nearly  equal  as  possible  to  the  resistance  of  the  external  part  of  the 
circuit. 

CLASSROOM   EXERCISES. 

1.  Determine  the  current  strength  of  a  battery  of  five  cells  joined 
in  parallel,  each  having  an  E.M.F.  of  2  volts  and  an  internal  resistance 
of  0.5  ohms,  (a)  when  the  external  resistance  is  0.1  ohm  ;  (6)  when 
the  external  resistance  is  500  ohms.      Ans.  (a)  10  amperes. 

(&)  Nearly  0.004  amperes. 

2.  Determine  the  current  strength  of  a  battery  made  up  by  coupling 


ELECTRIC   GENERATORS,  ETC.  483 

« 

the  same  5  cells  in  series,   (a)  when  the  external  resistance  is  0.1 
ohm ;  (b)  when  the  external  resistance  is  500  ohms. 

Ans.  (a)  3.846  +  amperes. 
(b)  0.0199+  amperes. 

3.  Connect  in  parallel  8  voltaic  cells,  each  having  an  E.M.F.  of  2 
volts,  and  an  internal  resistance  of  8  ohms,  the  total  external  resistance 
being  16  ohms.    Determine  the  current  strength.    Ans.  0.1176  amperes. 

4.  Compute  the  current  strength  of  the  same  8  cells  connected  in 
series.  Ans.  0.2  amperes. 

5.  Compute  the  current  strength  of  the  same  8  cells  when  joined 
in  two  rows,  each  row  being  a  series  of  four  cells,  and  the  rows  being 
joined  in  multiple  arc.  Ans.  0.25  amperes. 

6.  Each  of  ten  given  cells  has  an  electromotive  force  of  1  volt  and 
an  internal  resistance  of  5  ohms.     What  is  the  current  strength  of  a 
single  cell,  the  external  resistance  being  0.001  of  an  ohm  ? 

Ans.  0.19996  +  amperes. 

7.  The  ten  cells  above  mentioned  are  joined  in  parallel.     The 
external  resistance  is  0.001  of  an  ohm.     What  is  the  current  strength 
of  the  battery?  Ans.  1.996  +  amperes. 

8.  The  ten  cells  above  mentioned  are  joined  in  series,  the  external 
resistance  remaining  the  same.     What  Is  the  current  strength  of  the 
battery?  Ans.  0.19999  +  amperes. 

9.  What  is  the  current  strength  given  by  one  of  the  above  men- 
tioned cells  when  the  external  circuit  has  a  resistance  of  1,000  ohrns? 

Ans.  0.00099502  amperes. 

10.  When  the  ten  cells  are  joined  in  parallel  with  an  external  resist- 
ance of  1,000  ohms,  what  is  the  ampere  yield  of  the  battery? 

Ans.  0.0009995  amperes. 

11.  When  the  ten  cells  are  joined  in  series  with  an  external  resist- 
ance of  1,000  ohms,  what  is  the  current  strength  of  the  battery? 

12.  Six  cells,  each  having  an  E.M.F.  of  2  volts  and  an  internal 
resistance  of  0.8  of  an  ohm,  are  joined  in  series.     When  the  circuit 
is  closed,  the  wire  connections  aggregate  6  feet  of  No.  8  copper  wire, 
(a)  What  is  the  total  resistance  of  the  circuit?     (6)  What  is  Lhe  cur- 
rent strength  of  the  battery?  Ans.  (a)  4.80386  ohms. 

(6)  2.498  amperes. 

13.  Suppose  the  same  six  cells  to  be  joined  in  parallel,  the  wire 
resistance  being  the  same  as  before,     (a)  What  is  the  total  resistance 
of  the  circuit?     (b)  What  is  the  current  strength  of  the  battery? 

Ans.  (a)  0.1371  ohms. 
(b)  14.6  amperes. 


484 


SCHOOL  PHYSICS. 


14.  The  terms  "tandem"  and  "abreast"  are  sometimes  used  to 
describe  the  methods  of  grouping  cells  that  we  have  studied.     Which 
term  refers  to  grouping  in  series? 

15.  Two  voltaic  cells  give  equal  currents  on  "short  circuit,"  i.e., 
when  the  external  resistance  is  very  small.     How  can  you  experimen- 
tally ascertain  whether  their  electromotive  forces  are  equal? 

16.  Review  Laboratory  Exercises  4  and  7,  page  453,  and  indicate 
the  direction  of  the  magnetic  lines  of  force  of  the  rectangle,  of  the 
solenoid  and  of  the  magnet,  and  show  how  they  may  be  made  to 
account  for  the  observed  phenomena. 

Electromagnetic  Induction. 

Experiment  364.  —  For  a  galvanoscope  more  delicate  than  any  we 
have  yet  used,  procure  two  soft  pine  blocks,  4  cm.  square  and  2  cm. 
thick.  On  the  square  faces  of  each,  nail  or  glue  a  thin  piece  of  wood, 
6  cm.  square.  (These  pieces  may  be  cut  from  a  cigar  box.)  The 
channel  around  the  edges  of  the  blocks  will  be  2  cm.  wide  and  1  cm. 
deep.  Through  the  middle  of  each  block,  from  face  to  face,  bore  a 

hole  at  least  1.5  cm.  in  di- 
ameter. Wind  the  grooves 
full  of  No.  36  insulated  cop- 
per wire,  and  mount  the 
blocks,  A  and  B,  on  a  base- 
board with  their  opposing 
faces  about  1  cm.  apart,  as 
shown  in  Fig.  374.  Connect 
the  wires  of  the  two  coils 
so  that  a  current  flowing 
through  the  wire  will  circle 
around  the  coils  in  the  same 
FIG.  374.  direction;  i.e.,  connect  them 

in  series. 

Straighten  and  magnetize  four  or  five  pieces  of  watch  spring  each 
1.5  cm.  long,  and  fasten  them  with  thin  shellac  varnish  to  the  back  of 
a  piece  of  looking  glass,  1.5  cm.  square  and  as  thin  as  you  can  get. 
See  Fig.  375.  From  a  support  made  of  brass  wire,  suspend  the  mirror, 
M,  by  a  strand  of  silk,  the  lightest  that  will  carry  the  load.  A  single 
silk  fiber  may  be  strong  enough.  The  mirror  when  suspended  should 
hang  midway  between  the  two  coils,  and  directly  in  line  with  the  holes 
through  the  two  coils.  So  adjust  the  base  of  the  galvanoscope  that 


ELECTRIC   GENERATORS,   ETC. 


485 


the  coils  are  parallel  to  the  mirror  when  the  latter  is  freely  suspended 
between  them,  and  protect  the  apparatus  from  air 
currents  by  a  glass  cover.  A  feeble  current  pass- 
ing through  the  coils  will  deflect  the  delicately 
suspended  needles,  as  was  roughly  illustrated  in 
Experiment  315.  By  placing  a  bar  magnet  on  the 
table  so  as  partly  to  neutralize  the  directive  ten- 
dency of  the  terrestrial  magnetism,  the  sensitive- 
ness of  the  galvanoscope  may  be  increased. 

Stick  a  pin  into  the  end  of  the  base-board  and 
in  line  with  the  centers  of  the  openings  in  the 
coils,  as  appears  more  plainly  in  Fig.  376.  The 
eye  may  be  so  placed  that  the  pin  will  cover  its 
image  in  the  mirror.  The  slightest  deflection  of  F  —_ 

the  mirror  will  be  manifested  by  the  destruction 
of  this  coincidence.     Indicate  the  polarity  of  the  suspended  magnets 
by  marking  the  letters  N  and  S  near  the  edges  of  the  base-board 


FIG.  376. 

between  the  coils  .4  and  B.  Put  the  galvanoscope  into  circuit  with 
a  single  cell,  and  note  the  deflection  of  the  mirror.  Record  on  the 
base-board  of  the  instrument  the  fact  that  "  This  instrument  shows 
a  deflection  of  the  J\T  end  of  the  needle  toward  the  east  when  the  zinc 
plate  of  a  cell  is  connected  with  the  free  terminal  of  coil  B  (or  of  -A, 
as  the  case  may  be). 

Experiment  365. — Make  a  coil  of  wire  with  many  turns  of  No.  36 
insulated  copper  wire,  as  shown  at  H  in  Fig.  376.     The  coil  should 


486  SCHOOL  PHYSICS. 

have  an  internal  diameter  of  about  3  cm.,  and  a  cross-section  area  of 
at  least  1  sq.  crn.  Connect  the  terminals  of  the  coil  with  the  ter- 
minals of  the  galvanoscope.  Level  the  galvanoscope,  and  see  that 
its  needle-mirror  is  freely  suspended  as  directed  in  the  preceding- 
experiment.  Thrust  the  end  of  a  bar  magnet  at  least  1.5  cm.  in 
diameter  into  the  coil,  H,  thus  filling  the  coil  with  lines  of  force.  An 
electric  pulse  deflects  the  mirror  of  the  galvanoscope.  That  the 
deflecting  current  was  of  momentary  duration  is  shown  by  the  fact 
that  the  mirror  returns  to  its  first  position.  When  it  has  come  to  rest, 
remove  the  magnet  from  the  coil.  The  mirror  is  turned  the  other 
way  and  comes  to  rest  as  before,  thus  showing  that  the  direction  of 
the  second  current  was  opposite  to  that  of  the 
first,  and  that  its  duration  was  but  momentary. 
Repeat  the  experiment,  making  the  motions  of 
the  magnet  more  rapid.  Notice  that  the  pulses 
are  more  marked  than  before.  Repeat  the  ex- 
periment again,  using  a  low  resistance  solenoid 
that  carries  a  current  of  electricity,  as  shown 
in  Fig.  377,  instead  of  the  bar  magnet.  Then 
place  the  solenoid  inside  the  coil,  //,  and  break, 
and  make  the  battery  circuit.  Place  a  soft 
iron  rod  inside  the  solenoid  and  again  break 
and  make  the  circuit,  noticing  any  increase  in  the  deflections  of  the 
needle. 

That  the  galvanoscope  may  be  free  from  disturbing  magnetic 
influence,  see  that  all  knives,  keys,  watches  and  other  articles  of  iron 
or  steel  are  kept  at  a  considerable  distance  from  it,  and  that  the  coil,  H, 
is  so  far  removed  that  the  magnet  or  the  solenoid  may  not  have  any 
perceptible  direct  influence  upon  it.  It  will  be  well  to  wind  the  wire 
of  the  coil,  H,  upon  a  spool  as  shown  in  Fig.  378. 

388.  Induced  Currents.  —  When  the  number  of  mag- 
netic lines  of  force  that  pass  through  a  closed  coil  of  wire 
is  changed,  as  in  Experiment  365,  pulses  of  electricity  are 
generated  in  the  coil.  The  rapidity  with  which  the  coil 
is  filled  or  emptied  has  a  marked  effect  upon  the  intensity 
of  the  pulses  generated.  These  momentary  currents  are 
said  to  be  induced  in  the  coil;  i.e.,  they  are  induced  currents. 


ELECTRIC   GENERATORS,   ETC. 


487 


Experiment  366.  —  Connect  the  coil,  H  (Fig.  376),  to  the  galvano- 
scope,  G.     Make  another  coil  of  No.  20  insulated  copper  wire,  the 
same  size  as  H,  and  call  it  A.     Connect  A  with  the  battery,  and  deter- 
mine, by  the  corkscrew  rule,  which  side  of  it  is  north,  and  so  mark  it. 
Consider  the  deflections  of  G  to  the  right  as  + ,  and  deflections  to 
the  left  as  — .     Consider  lines  of  force  going  through  H  from  its  upper 
side  as  + ,  and  lines  that  flow  in  the  opposite  direction  as  — . 
Bring  the  north  end  of  a  magnet  to  the  coil,  H. 
"        "    south    "     "  "        "        "     "      "      " 
"        "    north  side  of  the  coil  A  to  the  coil,  H. 
"        "    south    "     "     "      "     "   "     "      "     " 
Lay  A,  north  side  down  upon  H,  and  make  the  circuit. 
"A,      "        "        "         "       "     "    break    "        " 
"    A,  south    "        "         "       "     "     make    "        " 
••      1        ••        ••        ••         "       '•     "     break    "        " 

In  each  of  these  cases,  record  the  deflection  of  G,  and  the  direction 
of  the  lines  of  force  passing  through  H.  When  a  magnet  is  used,  the 
direction  of  the  flux  may  be  determined  by  the  marked  polarity  of 
the  magnet.  When  the  coil,  -4,  is  used,  the  direction  of  the  flux  may 
be  determined  by  the  corkscrew  rule.  Remember  that  there  can  be 
no  deflection  of  G  without  a  change  in  the  number  of  lines  of 
force  in  H.  In  each  case,  record  your  answer  to  these  two  ques- 
tions :  — 

(1)  Was  there  an  increase  or  decrease  in  the  flux  of  force  in  Hf 
(*2)  What  deflection  of  G  results  from  an  increase  of  that  flux  in 
H,  and  what  from  a  decrease  ? 

Experiment  367.  —  Place  a  soft  iron  core  in  the  coil  H  as  shown  in 

Fig.  378,  and  repeat  Experiment 
366.  Notice  that  the  deflections 
are  now  much  more  marked. 


FIG.  379. 


FIG,  378. 


Experiment    368.  —  Place    the 
coil,  H,  in  circuit  with  a  telephone 


488  SCHOOL  PHYSICS. 

receiver  instead  of  the  galvanoscope.  When  the  circuit  of  A  is  made 
or  broken,  a  distinct  click  may  be  heard  in  the  receiver  which  is  a 
delicate  detector  of  pulses  of  electricity.  One  may  be  bought  at  a 
low  price,  or  borrowed. 

389.  Laws  of  Induced  Currents. — The  following  laws 
have  been  established  :  - 

(1)  An  increase  in  the  number  of  the  lines  of  force  pass- 
ing through  a  closed  coil  induces  a  current  in  one  direction 
through  the  wire  of  the  coil;  a  decrease  in  the  number  of 
the  lines  of  force  induces  a  current  in  the  other  direction. 

(2)  The  electromotive  force  of  the  induced  currents  de- 
pends upon  the  rapidity  of  change  in  the  number  of  lines 
of  force  that  pass  through  th3  coil. 

390.  The  Magneto.  —  A  number  of  permanent  magnets 
might  be  fastened  to  a  wheel  so  that  the  revolution  of  the 
wheel  would  carry  the  ends  of  the  magnets  in  front  of  a 
closed  coil  of  wire,  corresponding  to  the  coil,  H,  of  our 
recent  experiments.     As  each  magnet  approaches  the  coil, 
a  current  would  be  generated  within  the  coil ;  as  it  recedes 
from  the  coil,  a  current  of  opposite  direction  would  be 
generated  in  the  coil.     We  should  thus  obtain  an  alter- 
nating current  of  electricity  from  mechanical  power.    Such 
a  device  for  inducing  electric  currents  in  wire  coils  or  bob- 
bins, by  variations  in  the  relative  positions  of  the  coils  and 
of  permanent  magnets,  is  called  a  magneto-electric  machine, 
or  simply  a  magneto. 

(a)  The  fundamental  process  in  the  generation  of  electric  currents 
from  mechanical  power  consists  in  revolving  closed  conductors  in  a 
magnetic  field  in  such  a  way  as  to  vary  the  number  of  lines  of  force 
passing  through  them,  i.e.,  by  successively  filling  and  emptying  closed 
coils.  The  mechanical  motion  may  move  the  coils,  or  the  source  of 


ELECTRIC   GENERATORS,   ETC.  489 

the  magnetic  flux,  or  it  may  simply  move  a  mass  of  iron  that  forms  a 
ready  path  for  the  lines  of  force.  The  magneto  made  it  practicable 
to  obtain  electric  currents  from  mechanical  power,  an  advance  step 
because  mechanical  power  is  cheaper  than  the  chemicals  used  in  a 
voltaic  battery.  The  magneto  is  of  great  historical  interest,  but  it  has 
been  largely  displaced  by  the  more  efficient  dynamo. 

391.  The  Dynamo,  or  dynamo-electric  machine,  differs 
characteristically  from  the  magneto  in  that   the  former 
employs  a  field  of  force  due  to  the  influence  of  electro- 
magnets, while  the  latter  utilizes  permanent  magnets. 

392.  The   Simple  Dynamo.  —  Of  course,  it  makes  no 
difference  whether  the  coil  or  the  flux  of  force  moves, 
provided  that  the   num- 
ber of  lines  of  force  that 

pass  through  the  coil  is 
continually  changing. 
Suppose  a  single  loop  of 
wire  to  turn  upon  a  hori- 
zontal axis,  and  between 

FIG.  i>60. 

the  opposite  poles  of  two 

magnets,  iVand  $,  as  shown  in  Fig.  380.  When  the  loop 
stands  in  a  vertical  plane,  as  indicated  by  the  heavy  black 
line,  the  magnetic  lines  of  force  between  the  pole-pieces 
thread  through  the  loop  in  the  greatest  possible  number. 
When  the  loop  has  been  turned  upon  its  axis  through 
ninety  degrees,  until  it  lies  in  a  horizontal  plane,  as  indi- 
cated by  the  dotted  lines  in  the  figure,  the  lines  of  force 
run  parallel  to  the  plane  of  the  loop,  and  none  thread 
through  it.  During  this  quarter  revolution  of  the  loop, 
the  number  of  lines  of  force  that  pass  through  the  loop 
was  decreasing,  and  an  electric  current  was  thereby  in- 


490  SCHOOL  PHYSICS. 

duced  in  the  loop,  as  indicated  by  the  arrows.  During  the 
next  quarter  revolution  of  the  loop,  the  number  of  lines  of 
force  threading  the  loop  was  increasing,  but  as  they  passed 
through  the  loop  from  the  other  side,  the  current  induced 
in  the  loop  had^the  same  direction  as  before.  During  the 
next  half  revolution,  the  induced  current  will  flow  through 
the  loop  in  the  opposite  direction.  The  current,  therefore, 
reverses  twice  for  each  revolution  of  the  loop. 

393.  The  Direct  Current  Dynamo,  one  of  the  most  im- 
portant of  the  modern,  practical  devices  for  the  trans- 
formation of  mechanical  into  electrical   energy,  consists 
essentially  of  three  parts :   an  armature  made  of  coils  of 
wire,  which  may  be  revolved  in  a  magnetic  field,  and  thus 
successively  filled  with  lines  of  force  and  emptied  of  them  ; 
a  commutator  for  giving  a  uniform  direction  to  the  alter- 
nating currents  induced  in  the  coils  by  their  rotation  in 
the  field  of  force ;   and  a  large  electromagnet  as  a  source 
of  flux  of  force. 

394.  The  Armature.  —  If  the  revolving  coil  is  composed 
of  many  turns  of  wire  instead  of  a  single  loop,  the  electro- 
motive force  generated  by  the  revolution  will  be  multi- 
plied by  the  number  of  turns.     If  the  loop  is  filled  with 
soft  iron,  which  has  a  greater  magnetic  permeability  than 
air,  the  number  of  lines  of  force  gathered  into  the  space 
traversed  by  the  coil  will  be  increased,  and  the  electric 
effect  thereby  augmented.     A  soft  iron  cylinder  or  ring 
upon  which  coils  of  insulated  copper  wire  have  been  wound 
and  arranged  for  rapid  rotation  in  a  magnetic  field  is  called 
an  armature. 

(a)   The  Siemens  or  shuttle  armature,  represented  in  Fig.  381, 


ELECTRIC   GEJsTJRATORS,   ETC. 


491 


consists  of  a  coil  of  wire  wound  in  two  broad  grooves  plowed  on  op- 
posite sides  of  an  iron  cylinder.  Such  armatures  are  largely  used  in 
the  magnetos  used  for  "  calling  up  "  on  telephone  circuits,  but  they 
are  not  well  adapted  for  large  currents,  because  the  "  local  currents  " 


FIG.  381. 

(often  called  Foucault  currents)  generated  in  the  iron  core  absorb 
energy,  and  transform  it  into  heat.  This  heat  increases  the  internal 
resistance  of  the  coil,  and  is  objectionable  in  other  ways.  Moreover, 
with  such  an  armature,  the  current  falls  to  zero  twice  every  revolu- 
tion and,  for  many  purposes,  such  a  current  is  useless. 

(ft)  The  drum  armature  differs  from  the  shuttle  armature  chiefly  in 
that  it  employs  many  coils  instead  of  one.  The  cylindrical  iron  core 
is  made  of  thin  disks  of  soft  iron  insulated  from  each  other,  thus  min- 
imizing the  "  local  currents  "  and  the  heating  effects  thereof.  The 
insulation  for  this  purpose  sometimes  consists  of  tissue  paper,  some- 
times of  varnish,  and  sometimes  only  of  the  oxidation  on  the  surfaces 
of  the  metal.  On  the  cylinder  thus  built  up,  many  separate  coils  are 
wound  lengthwise,  as  is  shown  in  Fig.  382.  These  separate  coils  are 


FIG.  382. 

joined  in  series,  and  the  several  junctions  connected  to  insulated  bars, 
the  extremities  of  which  are  grouped  around  the  shaft  of  the  arma- 
ture as  shown  at  the  left  of  the  figure.  Brass  bands  around  the  out- 
side of  the  cylinder  hold  the  coils  in  place. 

(c)  The  Brush  or  ring  armature  consists  of  eight  or  more  coils 
wound  in  grooves  upon  an  annular  core,  as  shown  in  Fig.  383.  The 
core  is  laminated,  i.e.,  built  up  by  winding  a  thin  band  or  ribbon  of 


492 


SCHOOL  PHYSICS. 


soft  iron  in  successive  layers,  each  layer  being  insulated  from  the  next. 

The  wedge-shaped  projections  that  separate  the  coils  are  made  by 

thin  pieces  of  iron  placed  cross- 
wise between  successive  layers 
of  the  long  band  as  the  ring  is 
built  up.  Coils  radially  oppo- 
site are  joined  in  series,  and 
the  terminals  of  each  such  pair 
are  carried  to  the  commutator 
on  the  shaft  of  the  armature. 

(d)  Armature  coils  are  some- 
times wound  upon  arms  or 
spokes  that  project  radially 
from  a  central  hub,  or  are  set 
in  succession  on  the  face  of  a 

disk  and  near  its  circumference. 
FIG.  383. 

395.  The  Commutator.  —  If  the  connections  of  the  arma- 
ture coils  are  reversed  at  the  moment  when  the  current  in 
the  coils  is  reversed,  the  induced  currents  will  all  flow  in 
the  same  direction  in  the  external  circuit.  The  special 
device  for  thus  changing  the  connections  of  armature  coils 
is  called  a  commutator. 

(a)  The  commutator  of  the  Siemens  armature  consists  of  the  two 
halves  of  a  metal  collar  around  the  armature  shaft,  and  two  metal 
strips  or  "  brushes."  The  two  halves 
of  the  collar,  i.e.,  the  "  commutator 
segments,"  m  and  n,  are  separated  from 
the  shaft, s,  that  carries  them  by  a  bush- 
ing of  insulating  material,  and  are  sepa- 
rated from  each  other  as  shown  in  Fig. 
384.  One  end  of  the  armature  coil  is 
connected  with  one  segment,  and  the 
other  end  with  the  other  segment. 
The  brushes,  bb',  are  held  by  fixed 
supports  so  that  their  free  ends  rest  FlG-  384- 

lightly  on  the  segments.      The  points   of  contact  are  diametrically 
opposite. 


ELECTRIC   GENERATORS,   ETC. 


493 


Consider  b  and  b'  the  terminals  of  the  dynamo,  and  that  they  are 
connected  by  a  wire  that  constitutes  the  external  circuit.  Remember 
that  m  and  n  are  connected  through  the  armature  coil.  Assume  that 
the  connections  of  the  terminals  of  the  armature  coil  with  the  commu- 
tator segments  are  such  that  current  flows  through  the  coil  and  passes 
out  by  way  of  n  and  b.  As  the  armature  is  turned  a  little  further, 
the  current  in  the  coil  is  reversed,  and  flows  out  through  ?;i  instead  of  n. 
But  the  same  rotation  of  the  shaft  that  carries  both  the  armature  and 
the  commutator  has  now  brought  m  into  contact  with  b  so  that  the 
current  continues  to  flow  through  b  which  thus  remains  the  -f  ter- 
minal as  long  as  the  shaft  is  turned  in  the  direction  indicated  by  the 
arrow. 

(6)  There  are  many  different  ways  of  connecting  armature  coils 
with  their  commutators,  each  one  of  which  may  call  for  careful  study. 
The  following  may  be  taken  as  typical  of  most  of  them  :  in  Fig.  385, 
the  numbered  loops  represent  the  armature  coils  joined  in  series  as  in 
the  ring  armature.  The  heavy  broken  circle  represents  commutator 
segments  on  which  rest  the  ends  of  the  brushes,  b  and  b'.  The  brushes 
divide  the  coils  into  two  sec- 
tions. In  the  figure,  coils 
numbered  2,  3,  4,  5,  6,  and  7 
constitute  the  right-hand  sec- 
tion, and  coils  8,  9,  10,  11, 
12,  and  1  constitute  the  left- 
hand  section.  The  six  coils 
of  each  section  are  connected 
in  series,  and  the  two  sec- 
tions are  connected  in  par- 
allel. As  the  armature  turns 
between  the  pole-pieces,  N 
and  S,  and  in  the  direction 
indicated  by  the  arrow,  the  currents  induced  in  the  coils  of  the 
right-hand  section  will  flow  in  the  direction  indicated  by  the  arrow- 
heads. At  the  same  time,  the  currents  induced  in  the  coils  of  the 
left-hand  section  will  flow  in  the  opposite  direction,  as  indicated 
by  the  arrow-heads.  Imagine  a  current  returning  from  the  external 
circuit  and  entering  the  generator  at  b',  the  negative  terminal.  It 
will  find  two  paths  of  equal  resistance,  one  through  the  right-hand 
section,  and  the  other  through  the  left-hand  section.  In  either  case, 
the  direction  of  the  current  freshly  induced  in  those  sections  coincides 


FIG.  385. 


494 


SCHOOL  PHYSICS. 


with  its  own.     It,  therefore,  divides  itself  equally  between  the  two 
paths  and  flows  from  the  generator  at  b,  the  positive  terminal. 

396.  The  Field  Magnet.  —  The  electromagnet  that  sup- 
plies the  flux  of 
force  must  have  a 
current  to  excite 
it.  This  current  is 
sometimes  supplied  from  an 
outside  source,  as  is  dia- 
grammatically  shown  in  Fig. 
386.  Such  a  dynamo  is  said 
to  be  separately  excited. 
Often  all  of  the  current 
from  the  armature  is  carried 
around  the  coils  of  the  field 
magnet,  thus  forming  a 
series  dynamo,  as  is  shown  in  Fig.  387.  Sometimes  a 
part  of  the  current  from  the 
armature  is  carried  through  a 
shunt  circuit  consisting  of  many 
turns  of.  wire  that  is  smaller  than 
the  wire  of  the  main  circuit,  as 
is  shown  in  Fig.  388.  Such  a 
dynamo  is  said  to  be  shunt  wound. 
Sometimes,  for  purposes  of  regu- 
lation, the  field  magnet  is  encir- 
cled by  both  series  and  shunt 
coils,  as  is  shown  in  Fig.  389,  or 
by  either  of  those  with  a  separately  excited  coil.  Such 
a  dynamo  is  said  to  be  compound  wound. 

For  arc  lighting,  a  current  that  is  constant  under  vary- 


FIG.  386. 


FIG.  387. 


ELECTRIC  GENERATORS,  ETC. 


495 


ing  load  is  needed  ;  it  is  generally  secured  by  a  "  regu- 
lator" connected  with  the  dynamo,  as  shown  at  R  in 
Fig.  442.  The  regulator  may  be  automatic  in  its  action. 
For  incandescence  lighting,  a  potential  that  is  constant 
under  varying  load  is  needed ;  it  is  generally  secured  by 
compound  winding. 


SHUNT  CIRCUIT 
FIG.  388. 


FIG.  389. 


(a)  When  the  armature  of  a  "self  exciting"  dynamo,  i.e.,  one  that 
has  not  an  exciting  current  from^an  external  source,  is  put  in  motion, 
the  feeble  residual  magnetism  of  .the  cores  of  the  field  magnets  induces 
feeble  currents  in  the  armature  coils.  These  currents  flow  around  the 
magnets,  intensifying  their  power,  and  thus  increasing  the  E.M.F. 
of  the  machine.  The  current  thus  strengthened  further  energizes 
the  field  magnet.  Thus,  the  machine  "builds  up"  its  current  until 
the  magnets  have  reached  the  limit  of  excitation.  Many  dynamos, 
especially  those  used  for  the  generation  of  alternating  currents,  have 
more  than  two  pole-pieces. 

(6)  Lines  of  force  generated  by  the  field  magnet,  and  that  do  not 
pass  from  pole  to  pole,  are  termed  the  stray-field  or  the  leakage  lines. 
The  stray-field  between  the  pole-pieces  and  the  bed-plate  of  a  dynamo 
may  become  the  source  of  serious  loss  and  annoyance. 

(c)  Fig.  390  represents  the  Brush  dynamo  complete.  A  shaft  runs 
through  the  machine  from  end  to  end,  carrying  a  pulley,  P,  at  one 
end,  a  commutator,  c,  at  the  other  end,  and  a  wheel  armature,  R,  at 


496 


SCHOOL  PHYSICS. 


the  middle.  The  armature  carries  eight  or  more  helices  of  insulated 
wire,  H  H,  connected  in  pairs  as  described  in  §  394  (c) .  As  the  shaft 
is  turned  by  the  action  of  the  belt  upon  the  pulley,  the  armature  and 
the  commutator  are  turned  with  it.  The  armature  coils  are  thus 
carried  rapidly  across  the  four  poles  of  the  field  magnets,  MM, 


FIG.  390. 

traversing  the  intenser  parts  of  the  magnetic  field,  and  cutting  the 
lines  of  force. 

CLASSROOM  EXERCISES. 

1.  What  is  an  induced  electric  current?     How  is  it  produced? 

2.  How  are  induced  currents  made  continuous? 

3.  Give  some  proof  that  the  condition  of  a  wire  when  it  closes  an 
electric  circuit  is  different  from  the  condition  of  the  same  wire  when 
the  circuit  is  open. 

4.  Why  are  the  field  magnets  of  dynamos  generally  provided  with 
iron  cores? 

5.  What  advantage  is  there  in  making  the  field-magnet  cores  of 
cast  iron  instead  of  pure  soft  iron  ? 

6.  Upon  what  does  the  E.M.F.  of  a  dynamo  depend? 

7.  What  is  the  difference  between  a  magneto  and  a  dynamo? 

8.  When  a  dynamo  is  in  operation,  its  field  magnets  are  likely  to 
become  heated.     Does  this  increa  >e  or  diminish  the  efficiency  of  the 
machine,  and  why  ? 

9.  How  are  the  field  magnets  of  a  shunt-wound  dynamo  energized? 


ELECTRIC   GENERATORS,  ETC.  497 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  A  1-ohm  resistance  coil  of  No.  30  iron 
wire ;  a  resistance  coil  of  No.  30  German-silver  wire ;  two  magneto- 
scopes;  voltaic  cells;  plates  of  antimony,  and  of  zinc,  and  of  copper; 
a  copper  cartridge-shell ;  hydrochloric  acid ;  pieces  of  electric  light 
carbon;  a  telephone  receiver;  German-silver  wire;  two  semicircles 
of  soft  iron ;  an  iron  rod  45  cm.  long;  a  brass  tube,  and  one  of  rubber. 

1.  Given  the  two  electrodes  of  a  concealed  voltaic  battery,  deter- 
mine which  of  the  wires  is  connected  to  the  zinc  plate. 

2.  Connect  a  Leclanche  cell  and  a  freshly  prepared  dichromate  cell 
in  parallel,  and  place   a  galvanoscope   in  the  circuit,  between  the 
carbons,     (a)  Determine   and  record  the   direction  of  the  current. 
(&)  Place  the  galvanoscope  between  the  zincs,  and  determine  the  direc- 
tion of  the  current,      (c)  Why  should  this  current  flow?     (rf)  Is  it 
advisable  to  connect  cells  that  are  dissimilar  in  parallel,  and  why? 
(e)  Suppose  the  E.M.F.  of  the  dichromate  cell  to  be  2  volts,  and  that 
of  the  Leclanche  cell,  1.42  volts.     Suppose  the  resistance  of  the  dichro- 
mate cell  to  be  0.6  of  an  ohm,  that  of  the  Leclanche  cell  to  be  0.8 
of  an  ohm,  and  that  of  the  wire  and  galvanometer  to  be  1  ohm.    What 
is  the  resultant  current  in  the  system?     Remember  that  when  two 
electromotive  forces  are  in  opposition,  their  difference  is  all  that  is 
available. 

3.  Prepare  a  voltaic  cell  by  immersing  a  strip  of  amalgamated  zinc 
in  a  copper  cartridge-shell  filled  with  dilute  sulphuric  acid.     Connect 
this  cell  in  parallel  with  a  large  copper  and  zinc  pair  and,  by  means  of 
the  galvanoscope,  determine  whether  either  cell  forces  current  over 
into  the  other.     Make  several  trials,  using  acid  of  the  same  strength 
in  both  cells.     If  carefully  done,  it  will  be  found  that  the  E.M.F. 's 
are  nearly  equal. 

4.  Form  a  cell  with  antimony  and  copper  plates,  and  dilute  sul- 
phuric acid.     Insert  a  galvanoscope  in  the  circuit.     Note  and  record 
the  deflection.     Prepare  a  jar  of  dilute  hydrochloric  acid.     Lift  the 
plates  from  one  jar  to   the   other   without   otherwise  changing  the 
apparatus.     Note  and  record  the  deflection.     Which  is  attacked  more 
vigorously  by  sulphuric  acid,  antimony  or  copper  ?    Which  by  hydro- 
chloric acid? 

5.  Provide  a  glass  tube  about  1  cm.  internal  diameter.    Insert  a 
wire  in  each  end,  and  fill  the  tube  with  pieces  of  pounded  electric  light 
carbqn.     Pass  a  current  from  a  cell  through  the  apparatus,  interpos- 

32 


498 


SCHOOL  PHYSICS. 


ing  a  low  resistance  galvanoscope.  By  means  of  a  wooden  rod,  com- 
press the  powdered  carbon.  Why  is  the  deflection  largely  increased  ? 
Why  is  a  low  resistance  galvanoscope  used? 

6.  Calculate  the  length  of  No.  30  iron  wire  that  has  a  resistance  of 
1  ohm.     Procure  the  wire,  and  wind  it  on  a  board,  being  careful  that 
adjacent  turns  do  not  touch.     With  this  addition  to  your  apparatus, 
determine  whether  the  resistance  of  a  telephone  receiver  is  greater  or 
less  than  an  ohm,  and  whether  it  differs  much  or  little  from  an  ohm. 

7.  Wind  4  ounces  or  more  of  No.  30  insulated  German-silver  wire 
upon  a  spool.     Connect  this  bobbin  in  series  with  a  single  cell  and 
a  low  resistance  galvanoscope.     Record  the  deflection  of  the  latter. 
Change  the  low  resistance  block  of  the  galvanoscope  for  one  of  high 
resistance.     Again   note    and   record  the    deflection.      Explain    the 
increased   deflection   of    the  needle  that  accompanies  the  increased 
resistance  of  the  circuit. 

8.  Prepare  two  semicircles  of  |-inch  soft  iron  rod,  two  inches  in 
diameter,  and  file  the  faces  smooth,  so  that  they  will  fit  together  nicely. 


FIG.  391. 

Prepare  two  bobbins  of  approximately  equal  weight,  one  made  of 
about  20  turns  of  No.  16  wire,  and  the  other  of  No.  30  wire,  both 
insulated.  Slip  the  bobbins  on  one  of  the  iron  semicircles.  Connect 
the  terminals  of  the  fine  wire  coil  to  those  of  the  mirror  galvanometer 
(see  Experiment  364).  Arrange  the  galvanometer  so  that  the  mirror 


ELECTRIC   GENERATORS,  ETC. 


499 


reflects  its  beam  upon  a  ground  glass  scale  about  a  meter  away,  as 
shown  in  Fig.  391.  A  thin  line  of  black  paint  drawn  vertically  across 
the  center  of  the  mirror  will  aid  in  exactly  locating  the  spot  of  light 
upon  the  scale.  Connect  the  terminals  of  the  coarser  coil  to  those  of 
a  single  cell.  Open  and  close  the  primary  circuit,  and  note  the 
magnitude  of  the  kick  of  the  galvanometer.  Repeat  with  the  other 
half  of  the  ring  in  place,  and  notice  that  the  deflection  is  increased. 
Explain  this  increase,  remembering  the  effect  of  permeability  upon 
the  number  of  lines  of  force  in  a  magnetic  circuit. 

9.  Take  a  rod  of  iron  \  of  an  inch  in  diameter  and  18  inches  long, 
and  wind  upon  one  end  a  primary,  such  as  was  used  in  the  ring  of 
Exercise  8  ;  upon  the  other  end  of  the  rod,  wind  a  secondary  coil.  By 
means  of  opening  and  closing  the  primary  circuit,  and  noticing  the 
deflection  of  a  galvanoscope  properly  connected  to  the  secondary, 
determine  at  what  points  along  the  rod  the  lines  of  force  are  the 
greatest  in  number.  Why  is  the  maximum  deflection  found  when 
.the  primary  and  secondary  are  close  together?  On  paper,  map  the 
lines  of  force  as  you  think  they  must  exist  in  space.  Cover  the 
primary  coil  with  a  piece  of  glass,  and  pass  a  current  of  ten  or  more 
amperes  through  it.  Sprinkle  the  glass  with  filings,  and  prove  or  dis- 
prove your  theory. 

10.  Clamp  to  a  vertical  board  two  magnet  bobbins  (see  Exercise  12) 
joined  in  series  as  shown  in  Fig.  392.  Support  one  end  of  the  arma- 
ture, bm,  by  an  elastic  band,  ab. 
Pass  a  current  through  the  bob- 
bins, and  notice  the  pull  upon 
ab.  Looking  at  the  upper  ends 
of  the  bobbins,  notice  whether 
the  current  circles  around  the 
two  bobbins  in  the  same  direc- 
tion or  not,  as  clockwise  or 
counter-clockwise.  Turn  one 
of  the  bobbins  upside  down, 
changing  the  connections  in 
this  respect.  Ascertain  which 
connection  gives  the  greater 

pull  upon  the  armature,  bm,  and,  with  the  bobbins  thus  joined,  bring 
the  movable  soft  iron  yoke,  cd,  into  position  as  shown  in  the  figure. 
Explain  why  this  improves  the  magnetic  circuit,  so  that  the  upper 
armature  is  pulled  harder  than  before,  and  probably  drawn  down 


FIG.  392. 


500  SCHOOL  PHYSICS 

with  a  sharp  click.    Remember  that  all  magnetic  circuits  tend  to  con- 
tract themselves,  and  to  make  their  reluctance  as  small  as  possible. 

11.  Prepare  an  exploring  coil  with  several  hundred  turns  of  No.  30 
insulated  copper  wire  and  an  internal  diameter  of  5  cm.     Place  this 
coil  in  the  field  of  a  strong  electromagnet,  connect  its  terminals  with 
those  of  a  telephone  receiver,  and. make  and  break  the  magnet  circuit. 
Determine  the  points  where  the  flux  is  the  heaviest  by  moving  the 
coil  about  and  repeating  the  experiment.     Be  sure  to  have  the  face  of 
the  coil  at  right  angles  to  the  supposed  direction  of  the  magnetic 
lines  of  force.     Mount  the  coil  on  a  stiff  wire  that  passes  through  the 
center  of  the  coil,  and  lies  in  the  plane  of  the  coil.     The  plane  of  the 
coil  may  be  easily  changed  in  the  magnetic  field  by  rolling  the  sup- 
porting wire  between  the  thumb  and  forefinger.     Place  the  face  of 

the  coil  in  the  position  that  you  think  is  at 
right  angles  to  the  lines  of  force  in  the 
location  you  have  chosen.  Make  and  break 
the  magnet  circuit,  and  notice  the  strength 
of  the  click.  Now  turn  the  coil  a  quarter 
turn  and  repeat.  If  you  have  estimated 
FIG  393^  rightly?  there  should  now  be  no  click.  Place 

the  magnet  on  a  piece  of  paper,  and  draw  a 
line  under  the  coil  parallel  to  its  face  whenever  you  find  a  position 
where  no  click  occurs,  and  thus  map  out  the  field.  Sprinkle  the  paper 
with  filings,  and  verify  your  map. 

12.  Make  two  magnetoscopes  like  that  shown  in  Fig.  373.     An 
ordinary  carriage-bolt  about  7  cm.  long  may  be  used  as  the  core,  and 
a  soft  iron  nut  may  answer  as  the  armature.     With  the  two  magnet- 
oscopes, a  voltaic  battery,  and  a  supply  of  insulated  No.  20  copper 
wire,  arrange  apparatus  so  that  you  can  exchange  telegraphic  signals 
with  another  pupil  at  another  table,  or  in  another  room. 

397.  The  Alternator  is  a  dynamo  designed  for  the  gen- 
eration of  alternating  currents.  It  has  collecting  rings 
instead  of  a  commutator  so  that  the  current  is  delivered 
just  as  it  is  generated  (§  395),  and  a  small  direct  current 
dynamo  for  energizing  its  field  magnets,  the  pole-pieces  of 
which  are  generally  very  numerous.  Fig.  394  represents 
one  form  of  the  machine. 


ELECTRIC   GENERATORS,   ETC. 


501 


FIG.  31M. 

398.  Tesla's  Oscillator  is  a  combined  prime  motor  and 
electric  generator,  and  produces  alternating  currents  with- 
out rotary  motion  of 
the  generating  coils. 
The  motive  force  may 
be  that  of  steam  or  of 
compressed  air.  The 
machine  is  represented 
in  section  by  Fig. 
395.  The  powerful 
field  magnets,  MM, 
are  excited  by  a  cur- 
rent from  an  outside  FIQ.  395. 


502  SCHOOL  PHYSICS. 

source.  The  generating  coils  are  mounted  on  the  piston- 
rod,  A,  and  rapidly  vibrate  back  and  forth  in  the  direc- 
tion BB,  and  in  the  powerful  magnetic  fields,  at  HH. 
The  oscillating  piston-rod  slides  endwise  in  its  supports 
at  BB.  The  action  of  the  motive  power  is  somewhat 
peculiar,  and  depends  largely  on  the  inertia  of  the  oscillat- 
ing parts.  The  stroke  of  the  piston-rod  is  from  g1^  to  f  of 
an  inch,  according  to  the  pressure  used  and  the  nature  of 
the  current  desired.  The  output  of  the  machine  relative 
to  its  weight  is  exceedingly  large,  and  the  machine  gives 
promise  of  commercial  value. 

Experiment  369.  —  Mount  a  metal  clock-wheel  upon  wooden  bear- 
ings, and  solder  to  its  axle  a  wire  crank  by  which  it  may  be  turned. 

Provide  two  metal  springs.  The 
upper  end  of  one  should  rest  upon 
the  toothed  edge  of  the  wheel,  and 
"  snap  "  from  one  tooth  to  the  next 
as  the  wheel  is  turned.  The  upper 
end  of  the  other  should  rest  on 
the  axle  of  the  wheel.  Consider  the 
fixed  ends  of  these  springs  as  the 
terminals  of  this  "interrupter." 

FIG  39G    "  *P\\.i  ^is  apparatus  into  the  circuit 

with  a  voltaic  battery  and  the  gat 

vanoscope  that  has  a  coil  of  No.  16  wire.  Turn  the  wheel,  and  no- 
tice the  deflection  of  the  needle. 

399.  Alternating  Currents  have  some  peculiar  properties 
largely  due  to  the  constantly  fluctuating  field  of  force 
that  surrounds  their  conductors.  The  pulsating  current 
produced  by  the  interrupter  has  many  of  the  properties 
of  the  alternating  current,  and  will  facilitate  our  investi- 
gations. 

(a)  The  current  does  not  wholly  cease  when  the  spring  of  the 
interrupter  snaps  from  tooth  to  tooth.  As  the  circuit  is  broken,  the 


ELECTRIC   GENERATORS,   ETC.  503 

encircling  magnetic  lines  of  force  (§  382)  are  decreased  in  number, 
and  that  very  decrease  tends  to  continue  the  current  as  explained  in 
§  400.  In  brief,  the  current  does  not  have  time  wholly  to  die  away 
before  the  spring  is  on  the  next  tooth  of  the  wheel. 

Self-induction. 

Experiment  370.  —  Double  a  piece  of  Xo.  24  insulated  copper  wire 
about  100  feet  long,  and  wind  it  upon  a  wooden  rod  as  shown  in 
Fig.  397.  Join  the  ends  of  this  wire  in  the  series  circuit  of  the 
apparatus  arranged  for  Experiment  369.  Turn  the  wheel  of  the  inter- 
rupter rapidly,  and  note  the  deflection 


of    the    galvanoscope.      Remove    the     I  J  J  J  J  J  J  J  J  J  J  _  I 
No.  24  wire  from  the  circuit,  straighten 
it,  and  wind  it  upon  an  iron  rod  so  as 

to  form  an  electromagnet.  Put  this  electromagnet  into  the  circuit, 
and  repeat  the  experiment.  Xotice  that  the  deflection  of  the  galvan- 
oscope is  less,  and  that  the  sparks  at  the  wheel  of  the  intewupter 
are  greater  than  before. 

Experiment  371.  —  Place  the  coil  and  core  of  Experiment  367  in  the 
circuit  of  a  voltaic  battery,  and  insert  a  galvanoscope  as  shown  at  G 

in  Fig.  398.  When  the  circuit  is  closed 
by  depressing  the  key,  K,  part  of  the 
battery  current  is  shunted  from  m  to  n 
through,  the  galvanoscope,  and  deflects 
its  needle.  Force  the  needle  back  to 
zero,  and  place  some  obstacle  to  prevent 
its  moving  again  in  that  direction,  but 
leaving  it  free  to  move  in  the  opposite 
FIG.  398.  direction.  Break  the  circuit  at  K,  and 

notice  that  the  needle  does  swing  in 

the  opposite  direction,  showing  that  a  current  passed  through  it  from 
n  to  m.  This  current  was  not  the  battery  current,  for  the  battery 
circuit  was  open. 

400.  Self-induction.  —  When  the  number  of  lines  offeree 
in  a  coil  is  increasing,  an  electromotive  force  opposite  to  that 
of  the  inducing  current  is  established,  thus  weakening  the  di- 
rect current;  when  the  number  is  decreasing,  an  electromotive 


504  SCHOOL  PHYSICS. 

force  that  coincides  in  direction  with  that  of  the  inducing  cur- 
rent is  established,  thus  strengthening  the  direct  current.  In 
consequence  of  this,  we  may  have  an  opposition  to  the 
current-How  other  than  the  resistance  of  the  circuit, 
namely,  the  opposing,  self-induced  electromotive  forces. 
The  coil  manifests  a  conservative  tendency,  opposing 
sudden  changes.  When  the  doubled  wire  of  Experiment 
370  was  wound  upon  the  wooden  rod,  every  part  of  it 
lay  adjacent  to  another  part  that  was  carrying  current 
in  the  opposite  direction.  The  magnetic  lines  of  force 
generated  by  one  part  neutralized  the  lines  of  force  that 
circled  in  the  opposite  direction  around  the  adjacent  part ; 
i.e.  the  circuit  was  non-inductive.  In  the  other  case,  the 
lines  of  force  circled  in  the  same  direction  around  adja- 
cent parts  of  the  wire,  and  assisted  each  other  in  setting 
up  an  opposing,  self-induced  electromotive  force  that 
greatly  weakened  the  current  that  produced  them.  In 
Experiment  371,  the  self-induced  electromotive  force  gen- 
erated by  the  action  of  the  several  turns  of  the  coil  upon 
one  another  at  the  moment  of  opening  the  circuit  acted 
through  the  coil  in  the  same  direction  that  the  battery 
current  did,  and,  consequently,  sent  an  induced  current 
through  the  galvanoscope  in  the  opposite  direction. 

(a)  Such  a  coiled  circuit  is  said  to  have  a  reactance.  This  reactance 
has  much  the  effect  of  resistance,  but  it  depends  upon  other  considera- 
tions, chiefly  the  frequency  of  the  pulsations,  and  upon  a  certain  con- 
stant called  the  coefficient  of  self-induction.  This  coefficient  depends 
upon  the  shape,  coiling,  and  coring  of  the  circuit  and,  in  practice,  is 
determined  only  by  experiment.  Self-induction  coefficients  are  meas- 
ured by  a  unit  called  the  henry. 

401.  Reactance  and  Impedance.  —  As  alternating  cur- 
rents are  fluctuating  in  value,  their  measure  must  be  that 


UNIVERSITY  OF 

DEPARTMENT  OF  PHYSIOS 
ELECTRIC   GENERATORS,   ETC.  505 

of  averages.  The  chosen  average  is  the  square  root  of 
the  arithmetical  mean  of  the  squares  of  all  its  values. 
This  "  square  root  of  a  mean  square  "  applies  to  current 
and  to  voltage,  0  and  E.  For  a  true  alternating  current 
(i.e.  one  that  increases  and  diminishes  by  what  is  called 
the  law  of  sines),  the  numerical  relations  may  be  repre- 
sented thus  : 


+  (2  TrnL)* 

in  which  R  represents  the  ohmic  resistance,  n  the  fre- 
quency of  alternation,  and  L  the  coefficient  of  self-in- 
duction. The  expression  2  irnL  represents  the  reactance. 


The  apparent  resistance,  i.e.,  VJR2  +  (27rnZ)2,  is  called  the 
impedance,  and  is  measured  in  ohms. 

(a)  The  mathematical  relations  of  resistance,  reactance  and  impe- 
dance may  be  easily  remembered  by  considering  the  first  and  second  of 
these  functions  as  the  two  sides  of  a  right  angled  triangle  of  which 
the  impedance  is  the  hypothenuse,  i.e.  the  "  square  root  of  the  sum  of 
the  squares  of  the  other  two  sides." 

Experiment  372.  —  Wind  about  twenty  turns  of  No.  18  insulated 
copper  wire  around  a  |-inch  iron  rod,  or  (preferably)  around  a  bundle 
of  iron  wires,  and  put  the  coil  into  circuit  with  a  pulsating  current. 
The  lines  of  force  inside  the  coil  and  in  the  core  fluctuate  in  value 
with  the  current.  On  the  outside  of  this  coil,  and  carefully  insulated 
from  it,  wind  300  or  400  feet  of  No.  28  insulated  copper  wire.  Place 
one  of  the  terminals  of  this  outer  or  secondary  coil  above  the  tongue, 
and  the  other  terminal  below  it.  When  the  pulsating  current  flows 
through  the  inner  or  primary  coil,  currents  are  induced  in  the  second- 
ary coil,  and  produce  distinct  shocks  in  the  tongue. 

402.  The  Transformer.  --By  suitably  winding  and 
coring  primary  and  secondary  coils,  an  alternate  current 
at  one  voltage  may  be  received  by  the  primary,  and  a 
current  at  a  voltage  higher  or  lower  as  desired  delivered 


506 


SCHOOL  PHYSICS. 


from  the  secondary.  When  the  primary  is  made  of  a  few 
turns  of  large  wire,  and  the  secondary  is  made  of  many 
turns  of  small  wire,  the  voltage  is  increased,  and  vice 
versa.  Coils  so  wound  and  properly  cored  are  called  trans- 
formers. 

(a)  Transformers  are  largely  used  when  currents  of  high  voltage 
are  to  be  carried  great  distances,  and  delivered  at  a  pressure  suitable 
for  use.  With  a  given  resistance  in  the  line,  the  loss  in  watts  is  less 
with  a  small  current  and  high  voltage  than  it  is  with  large  current 
and  low  voltage.  With  a  given  line  loss,  high  voltage  currents  enable 
the  use  of  small  conductors,  and  copper  wire  is  expensive. 

(6)  When  the  electric  energy  is  transformed  from  a  current  of  low 
voltage  and  many  amperes  to  one  of  high  voltage  and  few  amperes, 
the  apparatus  is  called  a  "  step  up "  transformer.  Similarly,  when 
the  voltage  is  decreased,  the  apparatus  is  called  a  "  step  down  "  trans- 
former. 

403.  The  Induction  Coil  is  a  modification  of  the  appa- 
ratus used  in  Experiment  372,  and  is  often  called  the 
Rhumkorff  coil.  Receiving  a  large  current  of  small 
electromotive  force,  it  delivers  a  small  current  at  a  high 
pressure,  sometimes  hundreds  of  thousands  of  volts,  i.e., 
it  is  a  "  step  up  "  transformer. 

(a)  In  the  diagram  shown  in  Fig.  399,  M  represents  a  core  of  iron 


FIG.  399. 


ELECTRIC   GENERATORS,    ETC. 


507 


wires  upon  which  is  wound  a  primary  coil  of  coarse  wire  that  is  in 
circuit  with  the  voltaic  battery.      In  this  primary  circuit,  are  a  com- 
mutator, c,  for  changing  the  direction  of  the  current,  and  an  automatic 
interrupter,  b.  Wound 
upon  the  primary  coil, 
and  very  carefully  in- 
sulated  from    it,  is  a 

•M 


V, 


FIG.  400. 


secondary  coil  made 
of  very  many  turns  of 
fine  wire,  the  termi- 
nals of  which  are 
marked  T  T .  If  the 
coil  is  designed  to  give 
sparks  between  T  and 
T',  the  condenser,  CC, 
is  added.  This  con- 
sists of  sheets  of  tin-foil  separated  by  sheets  of  paraffined  or  shellac- 
varnished  paper.  The  alternate  sheets  of  tin-foil  are  joined  in 
parallel;  the  two  groups  are  connected  to  the  primary  circuit  on 
opposite  sides  of  the  interrupter.  The  condenser  is  generally  placed 
in  the  base  that  carries  the  coil.  A  simple  form  of  the  instrument 
is  shown  in  Fig.  400. 

(b)  The  current  passes  through  the  commutator,  c,  up  the  post,  A, 
through  the  adjusting  screw,  d,  and  across  to  the  spring  interrupter,  b, 
which  rests  against  the  end  of  d,  and  is  carried  by  another  post,  as 
shown  in  Fig.  400.    Thence  it  passes  to  the  primary  coil,  magnetizing 
the  iron- core,  and  making  its  way  back  to  the  generator.     The  iron 
core  thus  magnetized  attracts  the  soft  iron  hammer  at  the  end  of  the 
spring,  thus  breaking  the  circuit  at  b.     When  the  current  is  broken, 
the  core  is  demagnetized,  and  the  elasticity  of  the  spring  throws  b 
against  the  end  of  d,  again  making  the  circuit.      Thus  the  spring 
vibrates  between  the  end  of  the  core  and  the  end  of  the  screw,  making 
and  breaking  the  circuit  with  great  rapidity,  and  inducing  currents  in 
the  secondary  coil.     Owing  to  the  permeability  of  the  iron  core  which 
intensifies  the  flux  of  force  through  the  coils,  and  to  the  great  number 
of  turns  in  the  wire  of  the  secondary  coil,  the  electromotive  force  of 
the  induced  currents  is  very  high. 

(c)  The  self-induction  of  the  primary  coil  when  the  circuit  is  made 
at  b  develops  a  counter  E.M.F.  that  opposes  the  battery  current,  and 
thereby  lessens  the  E.M.F.  of  the  induced  current.     When  the  circuit 


508  SCHOOL  PHYSICS. 

is  broken,  the  counter  E.M.F.  reinforces  that  of  the  battery  current,  so 
that,  for  an  instant,  the  latter  may  be  increased  by  its  own  interrup- 
tion. One  effect  of  this  is  to  strengthen  the  sparks  noticeable  at  b. 

(rf)  One  effect  of  the  condenser  is  to  make  the  interruption  of  the 
battery  current  at  b  more  abrupt  and,  therefore,  to  increase  the  E.M.F. 
of  the  induced  current.  Immediately  after  the  interruption  of  the 
battery  current,  the  condenser  sends  a  reverse  current  through  the 
primary  coil  and  battery,  thus  demagnetizing  the  core  more  rapidly, 
increasing  the  rate  of  change  in  the  intensity  of  the  flux  through  the 
coils  and,  in  this  second  way,  increasing  the  E.M.F.  of  the  induced 
current.  Consequently,  the  E.M.F.  of  the  direct  current  induced 
in  the  secondary  coil  when  the  primary  circuit  is  broken  is  higher 
than  the  E.M.F.  of  the  reverse  current  induced  in  the  secondary  coil 
when  the  primary  circuit  is  made. 

(e)  The  length  of  the  spark  depends  upon  the  E.M.F.  of  the  induced 
secondary  current.  The  difference  of  potential  necessary  to  produce  a 
spark  1  cm.  or  more  in  length  between  parallel  plates  in  air  under 
ordinary  barometric  conditions  is  about  30,000  volts  per  centimeter. 
For  shorter  sparks,  the  difference  of  potential  has  a  greater  value. 

High  Potential  Phenomena. 

Experiment  373.  — Connect  a  voltaic  battery  with  the  primary  of 
an  induction  coil.  Bring  the  terminals  of  the  secondary  within  a  few 
millimeters  of  each  other,  and  notice  the  rapid  succession  of  sparks 
that  strike  across  the  gap  filled  with  air,  one  of  the  best  of  insulators. 
With  a  good  coil,  plates  of  glass  and  other  non-conductors  may  be 
thus  perforated.  We  have  not  noticed  this  property  of  electricity 
before  because  we  have  not  had  a  current  of  sufficiently  high  E.M.F. 

Experiment  374.  — In  a  shallow  tin  pan  (e.g.,  a  common  pie-tin), 
melt  equal  quantities  of  rosin  and  shellac.  Stir  the  substances  to- 
gether, avoid  ignition  and  the  formation  of  bubbles,  and,  when  the 
tin  is  filled,  set  it  aside  to  cool.  Cut  a  disk  of  sheet  tin  a  little  less  in 
diameter  than  the  resin  plate,  and  fasten  a  piece  of  sealing-wax  at  its 
center  for  a  handle.  Whip  the  plate  briskly  with  a  catskin,  or  rub  it 
with  warm  flannel.  Place  the  tin  disk  upon  the  resin  plate,  and  touch 
the  former  with  a  finger.  Place  a  number  of  small  bits  of  paper  upon 
the  disk.  Lift  the  disk  by  its  handle ;  the  charged  paper  bits  are 
repelled.  Bring  a  knuckle  to  the  edge  of  the  disk ;  an  electric  spark 
may  be  seen.  Such  a  discharge  in  air  requires  a  force  of  about  130 


ELECTRIC   GENERATORS,    ETC. 


509 


electrostatic  units  per  centimeter  of  length,  although  the  E.M.F.  per 
unit  length  is  greater  for  small  than  for  great  distances.  The  disk 
may  be  charged  many  times 
without  repeating  the  excita- 
tion of  the  resinous  plate. 
The  apparatus  may  be  im- 
proved by  making  the  disk 
of  wood,  rounding  its  edge, 
covering  it  with  tin-foil,  and 
smoothing  down  the  latter 
with  a  paper-folder  or  a  finger- 
nail. 

404.  An    Electrophorus 

consists  of  a  plate  of 
resinous  material  or  of 
vulcanite  resting  on  a 
metallic  bed-piece,  and 
a  movable  metallic  cover 
provided  with  an  insu- 
lating handle.  It  is  used 
as  illustrated  in  the  preceding  experiment.  As  the  sur- 
face of  the  resin  plate  is  uneven,  the  metallic  cover  touches 
it  at  but  a  few  points ;  as  the  material  is  non-conducting, 
scarcely  any  electrification  passes  from  the  former  to  the 
latter.  The  two  disks  and  the  thin  layer  of  air  between 
them  constitute  a  condenser  (§  342).  The  negatively  elec- 
trified resin  plate  acts  by  induction  on  the  disk,  holding 
positive  electrification  "  bound  "  at  its  lower  surface,  and 
repelling  the  negative  which  escapes  through  the  finger. 
When  the  plate  thus  charged  is  removed  from  the  resin 
plate,  the  bound  electrification  is  set  free. 

405.  Electric  Machines  for  developing  statical  electrifi- 
cation in  large  quantities  depend  upon  either  friction  or 


FIG.  401. 


510 


SCHOOL  PHYSICS. 


induction   for   their   operation,    and   are   made   in   great 
variety. 


FIG.  402. 

(a)  The  friction al  electric  machine  usually  consists  of  a  plate  of 
glass,  A,  which  is  revolved  between  stationary  cushions,  Z>,  the  sur- 
+  faces  of  which  are  cov- 

ered with  amalgam. 
The  parts  of  the  plate 
thus  positively  electri- 
fied are  successively 
brought  between  two 
metallic  combs,  F,  the 
pointed  teeth  of  which 
nearly  touch  the  plate. 
The  prime  conductor, 
P,  is  electrified  by  in- 
duction, the  negative 
electrification  escaping 
by  air-convection  from 
the  pointed  teeth  to 
the  oppositely  electri- 
fied plate,  thus  neutral- 
izing its  electrification 
and  leaving  the  prime 
conductor  positively 
charged.  The  negative  conductor,  N,  that  carries  the  cushions  is 


FIG.  403. 


ELECTRIC   GENERATORS,   ETC. 


511 


generally  connected  to  earth,  as  shown  in  Fig.  402.  The  potential 
energy  of  the  electrification  thus  obtained  is  the  equivalent  of  the 
kinetic  energy  expended  in  turning  the  crank,  minus  that  transformed 
into  useless  heat. 

(&)  The  induction  machines  may  almost  be  described  as  continuous 
electrophori.  The  Wimshurst  machine  (Fig.  403),  which  may  be  taken 
as  a  representative  of  the  class,  consists  for  the  most  part  of  two  equal 
glass  disks  that  revolve  in  opposite  directions.  Sector-shaped  strips  of 
tin-foil  are  fastened  to  the  outer  surfaces  of  the  plates,  and  act  as  car- 
riers of  electrification  and,  when  opposite  each  other,  as  field  plates  or 
inductors.  Two  conductors  are  placed  at  right  angles  to  each  other, 
obliquely  across  the  plates,  one  at  the  front  and  the  other  at  the  back. 
The  ends  of  these  conductors  carry  tinsel  brushes  that  lightly  touch 
the  sectors  as  they  pass.  The  discharging  circuit  is  provided  with 
combs  that  face  each  plate,  and  that  are  connected  with  small  Leyden 
jars.  The  distance  between  the  balls  of  the  discharging  circuit  may 
be  regulated  by  insulated  handles.  This  machine  is  almost  wholly 
free  from  "  weather  troubles." 

The  tin-foil  strips  or  carriers  on  the  rear  plate  of  a  Wimshurst 
machine  are  represented  in  Fig.  404  by  the  outer  row  of  strips ;  those 
on  the  front  plate,  by  the  inner  row.  The  diagonal  conductor  that 
faces  the  rear  plate  is  represented  by  cd  ;  the  one  that  faces  the  front 
plate,  by  ab.  The  strips  from 
which  the  arrows  proceed  are 
charged  positively ;  the  others, 
negatively.  The  strips  at  the 
top  of  the  rear  plate  are  repre- 
sented in  the  diagram  as  being 
positively  charged;  those  at 
the  bottom  as  being  nega- 
tively charged.  These  condi- 
tions are  reversed  for  the  front 
plate.  The  maximum  charge 
upon  one  of  the  tin-foil  strips 
or  carriers  is  represented  as 
six  units.  The  opposite  mo- 
tions of  the  two  plates  are 
represented  by  the  two  large, 

curved  arrows.  As  the  carrier  at  a  moves  into  the  position  shown  in 
the  diagram,  it  comes  under  the  inductive  influence  of  the  positively 


512  SCHOOL  PHYSICS. 

charged  carrier  opposite  it  on  the  rear  plate.  At  this  instant,  it 
touches  the  brush  of  the  diagonal  conductor,  and  a  transfer  of  posi- 
tive electrification  from  a  to  b  leaves  the  carrier  at  a  negatively 
charged.  At  the  same  instant  and  in  the  same  way,  the  carrier  at  b 
is  positively  charged.  Similar  effects  are  also  produced  in  the  carriers 
at  c  and  d.  Thus,  the  carriers  of  both  plates  come  to  m  and  n,  the 
combs  of  the  discharging  circuit,  similarly  charged,  positively  at  n, 
and  negatively  at  m.  The  inductive  action  of  these  carriers  upon  the 
discharging  circuit  electrifies  its  two  sides  oppositely. 

(c)  The  phenomena  of  static  electricity  that  may  be  exhibited  with 
a  machine  like  that  just  described  are  very  beautiful,  and  their  study 
is  very  enticing.  Some  of  them  were  known  to  man  before  the  dawn 
of  authentic  history.  Static  electricity  opens  a  field  for  deep  study 
that  has  been  of  great  value  in  theoretical  research,  and  is  now  full  of 
promise,  but  the  greater  and  rapidly  growing  industrial  importance  of 
current  electricity,  and  the  necessary  limitations  of  a  work  like  this, 
compel  the  author  to  refer  the  pupil  to  other  texts  for  a  fuller  discus- 
sion of  the  subject  than  he  can  give  here.  He  does  so  with  a  feeling 
of  sadness  that  utility  should  thus  dominate  beauty. 

High  Voltage  Currents. 

Experiment  375.  — AVind  several  turns  of  wire  upon  a  piece  of  glass 
tubing  inside  of  which  is  an  unmagnetized  sewing-needle.  Discharge 
a  Ley  den  jar  through  the  wire,  and  test  the  needle  to  see  if  it  has  been 
magnetized. 

Experiment  376.  —  Wind  ten  or  more  turns  of  insulated  wire,  No. 

22,  on  the  outside  of  a 
thin  glass  tumbler,  being 
careful  that  the  turns 
do  not  touch  each  other. 
A  coating  of  shellac  var- 
nish will  help  to  hold  the 
wire  in  place.  Wind  a 
smaller  coil  of  ten  or 
twelve  turns  of  similar 
wire,  bringing  one  end  of 
the  wire  up  through  the 
coil,  and  being  careful 
FIG.  405.  that  it  does  not  touch  any 


ELECTRIC   GENERATORS,   ETC.  513 

of  the  convolutions.  Tip  the  two  ends  of  this  wire  with  bullets,  and 
adjust  them  so  that  they  will  be  within  about  1  cm.  of  each  other. 
Place  the  second  coil  in  the  tumbler,  as  shown  in  Fig  405,  and  fill  the 
tumbler  with  high  grade  kerosene.  Connect  n,  the  lower  end  of  the 
outer  wire,  with  the  tin  pan  of  the  electrophorus.  Charge  the  disk 
of  the  electrophorus,  and  discharge  it  through  TO,  the  upper  end  of  the 
outer  coil.  Notice  the  spark  between  the  terminals  of  the  inner  coil. 
Support  an  iron  rod  inside  the  inner  coil,  being  careful  that  it  does 
not  touch  the  wire.  Repeat  the  experiment,  and  notice  that  the 
"  striking  distance  "  between  the  terminals  of  the  inner  coil  may  be 
increased. 

Experiment  377.  —  Connect  one  terminal  of  the  outer  coil  of  the 
apparatus  used  in  Experiment  376  to  a  terminal  of  the  secondary  of 
an  induction  coil.  Set  the  latter  in  operation,  and  discharge  the  other 
terminal  of  its  secondary  into  the  other  terminal  of  the  outer  coil  of 
the  tumbler.  Notice  the  series  of  sparks  between  the  terminals  of  the 
inner  coil  of  the  tumbler,  and  that  the  sparks  there  keep  step  with 
those  of  the  induction  coil. 

406.  Identity.  —  The  experiments  just  given  indicate 
the  remarkable  similarity  between  current  electricity  at 
high  voltage,  and  static  electricity.  Each  can  overcome 
the  enormous  resistance  of  an  insulator  like  the  air,  and 
each  lends  itself  to  electromagnetic  induction  in  the  same 
way.  Many  facts  tend  inevitably  to  the  conclusion  that 
the  two  kinds  of  electricity  are  identical. 

Nature  of  Electric  Discharge. 

Experiment  378.  —  Let  another  pupil  push  a  pin  through  a  visiting 
card.  Examine  the  card,  and  try  to  tell  from  which  side  of  the  card 
the  perforation  was  made.  Perforate  the  card  by  the  spark  of  an 
induction  coil,  examine  it  carefully,  and  try  to  tell  from  which  side 
the  perforation  was  made.  Similarly  examine  the  perforations 
made  in  a  card  by  the  discharges  of  an  electric  machine,  and  of  a 
Ley  den  jar.  What  do  you  infer  from  your  comparison  of  the  per- 
forations ? 

33 


514 


SCHOOL  PHYSICS. 


Experiment  379.  — Wind  two  or  three  layers  of  paper  upon  MN 
(Fig.  406),  a  bar  of  soft  iron,  and  about  fifty  turns  of  No.  22  insulated 
copper  wire  upon  the  paper.  Twist  loops  in  the  wire  at  A  and  B.  Tip 
the  ends  of  the  wire  with  bullets,  and  bring  them  very  near  each  other, 
as  at  C.  Ground  the  wire  at  B,  i.e.,  put  it  into  electrical  connection 

with  the  earth,  and  discharge 
the  electrophorus  or  a  Leyden 
jar  into  the  loop  at  A .  Notice 
the  sparks  at  C. 

Experiment  380.—  Straight- 
en the  wire    of    Experiment 


ooooooooooooc; c  i 


FIG.  407. 

379,  and  bend  it  into  a  long 
FlG  406  loop  returning  on  itself  as  in 

Fig.  407.  Adjust  the  knob 

terminals  at  c  for  the  same  distance  as  in  Experiment  379. 
Ground  b,  and  discharge  the  electrophorus  or  Leyden  jar  into  a,  as 
before.  You  will  find  great  difficulty  in  getting  a  spark  at  c,  and  may 
not  be  able  to  do  so  at  all. 

407.  Oscillatory  Discharge.  —  The  sparks  between  the 
knobs,  as  observed  in  Experiment  379,  show  that,  for 
some  reason,  the  electricity  preferred  the  path  through 
the  air  at  (7,  with  a  resistance  of  millions  of  ohms,  to  the 
path  through  the  wire  coiled  upon  MN,  with  a  resistance 
of  only  a  small  part  of  an  ohm.  If  the  flow  of  electricity 
from  a  point  of  high  to  one  of  low  potential  was  of  the 
nature  of  a  direct  current,  it  would  have  followed  Ohm's 
law,  and  passed  in  the  greatest  quantity  through  the  path 
of  least  resistance.  The  formula  applicable  in  such  a  case, 


ELECTRIC   GENERATORS,   ETC.  515 

offers  no   possible   explanation   of   the   phenomenon   ob- 
served. 

On  the  other  hand,  if  the  flow  was  like  that  of  an  alter- 
nating current,  it  would  be  governed  by  the  law  that  is 
expressed  thus  :  - 

0= 


The  fact  that  in  Experiment  380,  the  electricity  flowed 
through  the  wire  of  IOAV  resistance  instead  of  forcing  its 
way  through  the  enormous  resistance  of  the  air  as  it  did 
in  Experiment  379,  suggests  that  the  impedance  of  the 
circuit  coiled  around  the  iron  was  the  cause  of  the  appar- 
ently paradoxical  choice  of  path,  for,  when  we  got  rid  of 
that  impedance,  the  choice  was  what  we  should  have 
expected.  If  this  hypothesis  is  correct,  the  impedance  must 
have  been  very  great.  Studying  the  mathematical  expres- 
sion for  impedance,  as  given  above, 


we  notice  that  the  value  of  R  (the  resistance  of  the  wire) 
is  too  small  to  account  for  much  of  the  great  magnitude. 
The  rest  of  the  expression  is  the  square  of  the  reactance. 
Studying  the  values  therein  involved,  we  find  that  n  is 
the  only  factor  that  can  be  great  enough  to  account  for 
the  magnitude  assumed  for  the  impedance.  This  factor 
represents  the  frequency  of  -alternation,  and  its  magnitude 
must  be  measured  by  hundreds  of  thousands  in  order  that 
the  impedance  may  be  sufficiently  great  to  force  the  flow 
through  the  enormous  resistance  of  the  insulating  air  as 
was  done  in  Experiment  379. 

Recent  investigations  have  done  much  to  sustain  con- 


516  SCHOOL   PHYSICS. 

elusions  like  those  now  indicated,  and  to  justify  the  state- 
ment that  in  an  electric  discharge  the  flow  surges  back  and 
forth  thousands  of  times  in  the  brief  interval  measured  by 
the  duration  of  the  spark.  This  oscillatory  movement  is  a 
basis  of  important  investigations  now  in  progress,  and  maps 
out  the  line  by  which  static  electricity  may  become  a  thing 
of  practical  utility  as  well  as  of  phenomenal  beauty. 

408.  Atmospheric  Electricity.  —  The  surface  of  the  earth 
is  electrified.     The  electrification  is  generally  negative  but, 
in  time  of  rain,  it  may  become  locally  positive.     Moreover, 
the  electrical  density  varies  greatly  at  different  times  and 
places.       The  origin  of  the  earth's  electrification  is  not 
known  with  certainty,  but  it  "  is  influenced  very  largely, 
as  it  would  seem,  by  external  matter  somewhere  ;  probably 
at  a  distance  of  not  many  radii  from  its  surface." 

409.  The  Electrical  Function  of  Clouds  seems  to  be  to 
collect  and  to  concentrate  the  diffused  electrification  of  the 
atmosphere.       Suppose  a  thousand  spherical  watery  parti- 
cles, each  having  a  unit  charge,  to  coalesce  to  form  a  water- 
drop.     The  diameter  of  this  drop  will  be  ten  times  that  of 
a  single  particle,  its  capacity  will  be  ten  times  as  great, 
but  its  charge  will  be  a  thousand  times  as  great;  in  other 
words,  its   potential    will   be   increased   a   hundred-fold. 
The  condensation  and  aggregation  of  charged  vapor  parti- 
cles must  result  in  the  production  of  a  very  high  potential. 

410.  A  Lightning  Flash  is  simply  a  disruptive  discharge 
between  two  surfaces  oppositely  and  highly   electrified. 
The  discharge  may  be  from  cloud  to  cloud,  or  from  cloud 
to  earth.      The  charged  surfaces  and  the  intervening  air 
are  analogous  to  a  huge  Ley  den  jar.      Like  the  discharge 


ELECTRIC   GENERATORS,   ETC.  517 

of  the  jar,  the  lightning  flash  is  oscillatory.  A  lightning 
flash  a  kilometer  long  corresponds  to  a  difference  of 
potential  of  about  thirteen  million  electrostatic  units. 

(a)  The  sound  that  follows  a  lightning  flash  constitutes  thunder. 
The  sudden  expansion  and  compression  of  the  heated  air  along  the 
line  of  discharge  is  followed  by  a  violent  rush  of  air  into  the  partial 
vacuum  produced.  When  the  observer  is  about  equally  distant  from 
the  two  surfaces  between  which  the  discharge  takes  place,  a  short  and 
sharp  thunderclap  is  heard  ;  when  one  end  of  the  path  of  discharge  is 
considerably  further  from  the  observer  than  the  other,  so  that  there 
is  a  perceptible  difference  in  the  time  that  the  sound  requires  to  reach 
the  ear  from  the  different  parts  of  the  path,  there  is  a  prolonged  roll 
or  rattle.  Sometimes  near-by  hills  and  clouds  reflect  the  sound  so  as 
to  produce  a  continuous  or  rumbling  roar.  One-fifth  the  number  of 
seconds  that  intervene  between  seeing  the  flash  and  hearing  the  roar 
approximately  indicates  the  number  of  miles  that  the  observer  is  from 
the  discharge. 

(ft)  The  induced  charge  on  the  earth  tends  to  accumulate  on  build- 
ings, trees,  and  other  elevated  objects,  thus  reducing  the  thickness  of 
the  dielectric,  intensifying  the  attraction  between  the  opposite  elec- 
trifications, and  increasing  the  liability  of  such  elevated  bodies.  Sta- 
tistical studies  seem  to  show  a  minimum  liability  to  accident  from 
lightning  stroke  in  thickly  settled  communities,  and  that  the  danger 
in  the  country  is  five  times  as  great  as  that  in  the  city.  Such  studies 
have  also  shown  that  there  is  no  foundation  for  the  popular  notion 
that  "lightning  never  strikes  twice  in  the  same  place"  except  the 
fact  that  lightning  often  leaves  nothing  to  be  struck  a  second  time. 
At  the  same  time,  it  is  well  to  remember  that  "Heaven  has  more 
thunders  to  alarm  than  thunderbolts  to  punish,"  and  that  one  who 
lives  to  see  the  lightning  flash  need  not  concern  himself  much  about 
any  personal  injury  from  that  flash. 

Experiment  381.  —  Twist  together  two  wires,  one  of  iron  and  one 
of  German-silver,  and  attach  their  free  ends  to  the  terminals  of  a 
galvanoscope.  Heat  the  junction  of  the  two  wires.  The  deflection 
of  the  needle  indicates  that  un  electric  current  was  generated.  Cool 
the  junction  of  the  dissimilar  metals  with  ice.  The  opposite  deflection 
of  the  needle  shows  that  the  current  now  generated  flows  in  a  direc- 
tion that  is  the  reverse  of  the  first. 


518 


SCHOOL  PHYSICS. 


411.  Thermo-electric  Pile.  — Two  dissimilar  metals  joined 
and  used  like  those  of  Experiment 
381,  constitute  a  thermo-electric 
pair.  Antimony  and  bismuth 
are  the  metals  generally  used  for 
the  purpose.  Many  such  pairs 
connected  in  series  and  having 
their  ends  exposed  constitute  a 
thermo-electric  pile.  Such  a  pile 
with  conical  reflectors  is  repre- 
sented in  Fig.  408.  When  its 
terminals  are  connected  to  the 
terminals  of  a  delicate  galvano- 
scope,  the  combination  consti- 
tutes a  thermoscope  of  great  sensitiveness. 

CLASSROOM   EXERCISES. 

1.  (a)  How  is  impedance  measured?     (6)  How  is  the  coefficient  of 
self-induction  measured?     (c)  Upon  what  does  the  latter  depend? 

2.  Show,  by  the  formula  for  impedance,  that  the  static  discharge  is 
of  a  rapidly  alternating  nature. 

3.  Explain  self-induction.     How  does  it  interfere  with  the  flow  of 
an  alternate  current? 

4.  (a)  Define  reluctance,  and  write  the  mathematical  expression 
therefor.      (b)   Show  geometrically  the  relation  between  reactance, 
impedance  and  resistance. 

5.  Sketch  the  connections  of  the  induction  coil.    Explain  the  action 
of  the  automatic  current  interrupter. 

6.  Describe  the  electrophorus,  and  explain  its  action. 


FIG.  408. 


LABORATORY    EXERCISES. 


Additional  Apparatus,  etc.  —  A  gold-leaf  electroscope  in  which  the 
knob  shown  in  Fig.  315  is  replaced  by  a  metal  disk  about  15  or.  20  cm. 
in  diameter;  50  small  glass  tumblers;  sheet  zinc;  sheet  copper;  tin 
plate;  Geissler  tube ;  an  incandescence  electric •  lamp ;  rosin  or  pitch. 


ELECTRIC   GENERATORS,   ETC.  519 

1.  Place  50  small  glass  tumblers  in  a  circle.     Into  each  tumbler, 
put  a  small  strip  of  clean  zinc,  and  a  similar  strip  of  copper.     Nearly 
fill  each  tumbler  with  water,  and  connect  the  battery  in  series.    Solder 
a  thin  copper  wire  about  50  cm.  long  to  the  zinc  plate  at  the  end  of 
the  series,  and  a  similar  wire  to  the  copper  plate  at  the  other  end  of 
the  series.     Lay  a  'sheet  of  thin  paper  that  has  been  well  soaked  in 
melted  paraffine  upon  the  disk  of  a  gold-leaf  electroscope.      Place  an 
electrophorus  cover  upon  the   paraffined  paper,  thus  making  a  con- 
densing electroscope.    Bring  one  of  the  battery  terminals  into  contact 
with  the  disk  of  the  electroscope,  and  the  other  terminal  into  contact 
with  the  disk  of  the  electrophorus.    Remove  the  wires,  and  lift  the 
electrophorus  cover  and  the  paper  from  the  disk,  thus  reducing  the 
capacity  of  the  lower  disk  and  raising  its  potential.     If  you  notice 
any  evidence  of  an  electric  charge  on  the  leaves  of  the  electroscope, 
determine  whether  that  charge  is  positive  or  negative. 

2.  Substitute  dilute  sulphuric  acid  for  the  water  that  was  used  as 
the  exciting  fluid  in  the  "crown  of  cups  "  of  Exercise  1,  and  complete 
the  circuit  through  a  resistance  of  several  hundred  ohms.     By  a  wire, 
connect  a  point  in  this  circuit  near  the  terminal  zinc  with  the  disk  of 
the  electroscope,  arranged  as  in  Exercise  1.     Similarly,  connect  a 
point  in  this  circuit  near  the  terminal  copper  with  the  electrophorus 
cover.     Try  to  charge  the  electroscope  as  in  Exercise  1.      If  you  suc- 
ceed, test  the  character  of  the  charge,  and  record  your  conclusions  as 
to  a  permanent  difference  of  potential  at  different  points  in  the'circuit 
of  a  voltaic  battery. 

3.  Attach  a  Geissler  tube  to  the  secondary  terminals  of  an  induc- 
tion coil.     Put  the  coil  in  operation,  and  notice  the  discharge  through 
the  tube,  and  the  difference  from  its  discharge  through  air.     Measure 
the  maximum  length  of  the  spark  obtainable  with  the  coil,  and  com- 
pare it  with  the  length  of  the  longest  discharge  that  you  can  get 
through  a  Geissler  tube. 

Present  a  magnet  pole  to  the  Geissler  tube,  and  notice  the  deflection 
of  the  discharge.     Re- 
verse the  polarity  of 
the  primary  of  the  in- 
duction  coil.      Xotice 

that  the   discharge  is  FlG  409 

now  deflected    in    an 

opposite   direction.      Does  this   throw  any  light  on    the    question 
whether  the   alternating  pulses  of  the  induction  coil  are  of  equal 


520 


SCHOOL   PHYSICS. 


strength  or  not?  Study  the  discharge  through  the  tube  with  refer- 
ence to  the  different  appearances  of  the  two  ends  of  the  tube.  Reverse 
the  coil,  and  notice  the  corresponding  reversal  in  the  positions  of  the 
violet  tint  and  the  scintillations.  On  reversing  the  coil,  the  lights 
in  the  tube  reverse.  If  the  tube  was  excited  by  a  true  alternate  cur- 
rent, would  such  differences  be  noted  ? 

4.  Suspend  a  tin  plate  about  10  cm.  square  from  each  binding  post 

of  the  secondary  of  a  strong 
induction  coil,  as  shown  in 
Fig.  410.  Let  the  plates 
hang  parallel  to  each  other 
and  about  8  cm.  apart. 
Start  the  coil.  Darken  the 
room,  and  hold  a  small  Geiss- 
ler  tube  in  the  electrostatic 
field  of  force  between  the 
plates,  with  the  ends  of  the 
tube  near  but  not  touching 
FIG.  410.  them.  The  tube  glows 

brightly.     Touch  the  plates 

with  the  ends  of  the  tube.  Notice  the  increased  brightness.  Quickly 
lay  the  tube  in  a  dark  corner,  and  notice  the  after-glow. 

5.  Grasp  a  110-volt  incandescence  lamp  firmly  in  the  hand,  keep- 
ing the  fingers  away  from  the  brass  cap.     Let  some  one  else  charge  the 
lamp  with  an  electrophorous.     Discharge  the  lamp  by  touching  the 
brass  cap,  keeping  an  eye  on  the  filament.     When  the  discharge  takes 
place,  the  filament  swings  around  the  bulb  as  if  it  were  sweeping  off 
the  charge  from  the  surface  of  the  glass  and  delivering  it  to  the  cap. 
As  there  is  danger  of  breaking  the  filament,  it  is  well  to  use  an  old 
lamp.      Repeat  the  experiment  in  the  dark,  and  notice  the  brilliant 
glow  of  the  lamp  when  discharging. 

6.  Paste  strips  of  tin-foil  on  a  microscope  slide  as  shown  in  Fig. 
411.     Discharge  the  induction  coil  through  these  strips,  and  view  the 
spark  through  the  microscope  with  a 

f-inch  or  a  1-inch  objective.  Notice 
the  general  resemblance  of  the  dis- 
charge to  the  discharge  in  a  vacuum. 
Note  the  purple  vaporous  negative  pole, 
and  the  scintillating  positive  pole,  as  shown  in  Fig.  412.  Bring  the 
pointed  ends  of  the  tin-foil  strips  on  the  slide  as  near  together  as  you 


FIG.  411. 


ELECTRIC   GENERATORS,    ETC. 


521 


can  without  contact.  Focus  the  microscope  well,  using  a  i-inch  or 
a  i-inch  objective.  Be  careful  that  the  discharge  does  not  enter  the 
end  of  the  objective  instead  of  leaping  the  gap  between  the  strips, 
a  possible  circumstance  that  would  not  injure  you  as  much  as  it 


FIG.  412. 


would  your  experiment.  Watch  the  points  through  the  microscope, 
turn  on  the  current,  and  notice  that  the  negative  pole  is  rapidly  eaten 
away.  Quickly  reverse  the  connections  of  the  primary  switch,  and 
notice  that  what  was  the  positive  pole  is  now  eaten  away. 

7.  Connect  the  outside  coating  of  a  Leyden  jar  by  a  wire  to  one  of 
the  terminals  of  an  induction  coil.     Bring  the  knob  of  the  jar  near  the 
other  terminal  of  the  coil  and  allow  sparks  to  pass  between  them  for 
a  minute.     Remove  the  jar,  and  connect  its  two  coatings  with  the 
fingers.     A  smart  shock  shows  that  the  jar  is  charged.     Bring  the 
knob  of  the  jar  into  contact  with  the  free  terminal  of  the  coil  instead 
of  allowing  the  discharge  to  spark  across.     It  will  be  found  impossible 
thus  to  charge  the  jar.     Why? 

8.  Support  two  metal  balls,  a  and  b  (Fig.  413),  between  the  terminals 
of  an  induction  coil,  put  the  coil  in  operation,  and  determine  the  limit- 
ing length  of  the  discharge  between  the  balls.     Then  connect  a  Leyden 


522  SCHOOL   PHYSICS. 

jar  to  the  terminals,  as  shown  in  Fig.  413.     Start  the  coil  again,  and 

notice  that  the  spark  will 
not  strike  across  so  long  a 
gap,  but  that  it  is  a  much 
Hotter,  "  fatter  "  spark.  Open 
the  circuit  at  x,  and  insert 
the  oil  transformer  of  Exper- 
iment 376.  It  will  be  found 
to  work  in  a  satisfactory 
FlG-  413-  manner. 

9.  Devise  a  suitable  experiment  to  determine  whether  the  flame  of 
a  carbonaceous  substance,  e.g.,  rosin  or  pitch,  or  dry  air  is  the  better 
conductor  for  the  high  potential  discharge  between  the  terminals  of 
the  secondary  of  an  induction  coil.  Describe  the  experiment  in 
detail.  To  what  conclusion  does  your  experiment  lead  you? 

10.  On  a  thin  hard  rubber  or  glass  tube  10  cm.  long,  wind  evenly  a 
layer  of  No.  16  insulated  copper  wire.  Insulate  it  thoroughly,  and 
wind  on  a  secondary  coil  of  ten  layers  of  No.  30  insulated  copper  wire. 
Place  the  ends  of  the  secondary  wire  above  and  below  the  tongue,  or 
connect  them  to  the  terminals  of  a  telephone  receiver.  Pass  a  battery 
current  through  the  primary  coil.  On  making  and  breaking  the  pri- 
mary circuit,  electric  pulses  are  detected  in  the  secondary  circuit. 
Place  an  iron  core  in  the  tube.  The  pulses  are  much  increased  in 
intensity.  Why?  Slip  a  brass  tube  over  the  iron  core,  place  it  in 
the  rubber  tube,  and  repeat  the  experiment.  The  pulses  are  now  of 
the  same  intensity  that  they  were  before  the  core  was  inserted.  Slit 
the  brass  tube  along  its  length,  and  repeat  the  experiment.  The 
pulses  are  now  as  strong  as  they  were  before  the  tube  was  used. 
Remember  that  the  induced  current  acts  in  direct  opposition  to  the 
lines  of  force  inducing  it,  and  tends  to  neutralize  them.  Such  an 
induced  current  flows  through  the  brass  tube  which  corresponds  to 
a  closed  secondary  coil,  absorbing  energy,  and  tending, to  neutralize 
the  magnetic  effect  of  the  primary  current. 


ELECTRICAL   MEASUREMENTS. 


523 


III.    ELECTRICAL   MEASUREMENTS. 

412.  Electrostatic  Units  necessarily  relate  to  quantity, 
potential  difference,  and  capacity  ;  they  have  already  been 
denned.  Since 

Quantity  =  capacity  x  difference  of  potential, 
any  one  may  be  calculated  when  the  other  two  are  known. 

(a)  For  practical  convenience,  certain  multiples  and  submultiples 
of  these  absolute  C.G.S.  units  are  in  common  use  among  electricians. 
Their  names,  and  their  values  in  absolute  electrostatic  units  are  as 
follows :  — 


Denomination. 

Quantity 

Potential  difference 

Capacity 

Current 

Resistance 

Work  (volt-coulomb) 

Activity  (volt-ampere) 


Practical  Units. 

Name. 

Coulomb 

Volt 

Farad 

Ampere 

Ohm 

Joule 

Watt 


Value. 
3  x  109 
£x  10-2 
9  x  1C11 
3x  109 
|  x  ID-" 
107  ergs 
107  ergs  per  second 


(6)  Various  methods  have  been  devised  for  measuring  electrostatic 
quantity,  one  of  the  simplest  of  which  is  with  the  Kinnersley  electrical 
air-thermometer,  shown  in  Fig.  414.  When  a  spark  passes 
between  the  balls  within  the  larger  tube,  the  confined  air 
is  expanded,  and  the  liquid  column  in  the  smaller  com- 
municating tube  rises,  and  thus  approximately  indicates 
the  quantity  of  the  charge. 

(c)  Instruments  for  measuring  differences  of  potential  by 
electrostatic  action  are  called  electrometers.  The  gold-leaf 
electroscope  is  an  electrometer  when  it  is  used  to  indicate 
equality  of  potential  by  equality  of  divergence  of  the  leaves ; 
or  in  that  of  two  bodies  dissimilarly  electrified  by  bringing 
them  into  contact,  and  observing  zero  divergence.  One  of 
the  best-known  instruments  of  this  class  is  Coulomb's  torsion- 
balance,  which  consists  essentially  of  a  gilt  ball,  i,  carried  at  the  end 


FIG.  414. 


524 


SCHOOL   PHYSICS. 


of  a  horizontal  shellac  needle  that  is  suspended  by  a  fine  silver  wire 
from  the  top  of  a  tube  that  rises  from 
the  cover  of  the  enclosing  glass  cylinder. 
A  vertical  insulating  rod  passing  through 
the  cover  carries  a  handle,  a,  and  a  gilt 
ball,  e,  at  its  ends.  The  tube  is  turned 
until  i  just  touches  e.  When  the  ball,  e, 
is  electrified,  it  repels  i  through  a  certain 
angle.  This  angle  of  deflection  is  ap- 
proximately proportional  to  the  force  of 
repulsion,  and  the  force  is  proportional 
to  the  amount  of  electrification.  As  the 
capacity  of  the  ball  is  constant,  the 
charge  that  it  receives  must  vary  as 
the  potential  of  the  body  by  which  it 

was  charged. 
FIG.  415. 

413.  Electromagnetic  Units  constitute  a  system  based  on 
the  electromagnetic  actions  of  the  current.  The  C.G.S. 
electromagnetic  unit  of  quantity  is  the  quantity  which, 
flowing  per  second  through  a  circular  arc  a  centimeter  in 
length  and  a  centimeter  in  radius,  exerts  a  force  of  a  dyne 
on  a  unit  magnetic  pole  at  the  center.  The  C.G.S.  elec- 
tromagnetic unit  of  quantity  has  a  value  3  x  1010  times  as 
great  as  the  corresponding  electrostatic  unit,  a  ratio  that 
represents  the  velocity  of  light. 

(a)  This  ratio  or  its  square  applies  to  the  other  units,  so  that,  for 
the  practical  units,  we  have  the  following  values  in  absolute  electro- 
magnetic units :  — 


Coulomb 

Volt 

Farad 


10-1 
108 

io-9 


Ampere 
Ohm 


io-1 

IO9 


(6)  The  wonderful  advance  made  in  the  last  few  years  by  electrical 
science  is  largely  due  to  the  adoption  of' definite  electrical  units,  and 
the  general  practice  of  making  exact  electrical  measurements. 


ELECTRICAL  MEASUREMENTS. 


525 


414.  The  Galvanometer  is  an  instrument  for  determining 
the  strength  of  an  electric  current  by  means  of  the  deflection 
of  a  magnetic  needle  around  which  the  current  flows. 
When  a  galvanoscope  is  provided  with  a  scale  so  that  the 
deflections  of  its  needle  may  be  measured,  it  becomes  a 
galvanometer. 

(a)  The  astatic,  galvanometer  consists  of  an  astatic  needle  supported 
by  an  untwisted  liber  so  that  one  of  its  needles 
is  nearly  in  the  center  of  the  coil  through 
which  the  current  passes  while  the  other 
needle  is  just  above  the  coil.  When  the  deflec- 
tions of  the  needle  are  less  than  10°  or  15°,  they 
are  very  nearly  proportional  to  the  strengths  of  the 
currents  that  produce  them.  A  current  that  de- 
flects the  needle  6°  is  about  three  times  as 
strong  as  one  that  deflects  it  2°. 

(6)  The  tangent  galvanometer  consists  of  a 
very  short  magnetic  needle  suspended  so  as 
to  turn  in  a  horizontal  plane,  and  with  its 
point  of  support  at  the  center  of  a  vertical 

hoop   or 


FIG.  416. 


FIG.  417. 


coil  of  copper  wire 
through  which  the  current  is 
passed.  The  diameter  of  the 
hoop  or  coil  is  not  less  than 
ten  times  the  length  of  -the 
needle.  Owing  to  the  short- 
ness of  the  needle,  pointers  of 
aluminium  or  of  glass  fiber  are 
generally  cemented  across  it  at 
right  angles,  as  shown  in  Fig. 
417.  In  use,  the  hoop  is  placed 
in  the  plane  of  the  magnetic 
meridian,  the  current  that  is 
to  be  measured  is  sent  through 
the  hoop,  and  the  deflection  of 
the  needle  is  read  from  the 
scale.  The  strength  of  the  cur- 
rent is  proportional  to  the  tangent 


526  SCHOOL  PHYSICS. 

of  the  angle  of  deflection.  For  example,  suppose  that  a  certain  cur- 
rent gives  a  deflection  of  15°,  and  that  another  current  gives  a  deflec- 
tion of  30°.  The  amperes  are  not  in  the  ratio  of  15  :  30  but  in  the 
ratio  of  tan  15° :  tan  30°.  The  values  of  such  tangents  may  be 
obtained  from  a  table  of  natural  tangents.  If  a  current  of  known 
strength,  C,  gives  a  deflection  of  m  degrees,  and  another  of  unknown 
strength,  x,  gives  a  deflection  of  n  degrees,  the  value  of  x  may  be 
found  from  the  proportion,  — 

C  :  x  : :  tan  m  :  tan  n. 

A  table  of  natural  tangents  is  given  in  the  appendix. 

(c)  Any  sensitive  galvanometer,  the  needle  of  which  is  directed  by 
the  earth's  magnetism,  and  in  which  the  frame  on  which  the  coils  are 
wound  is  capable  of  being  turned  round  a  vertical  axis,  may  be  used 
as   a  sine  galvanometer.      The   coils   are   set  parallel  to  the   needle 
(i.e.,  in  the  magnetic  meridian).     The  current  is  then  sent  through 
the  coils,  deflecting  the  needle.     The  coil  is  then  turned  until  it  over- 
takes the  needle,  which  once  more  lies  parallel  to  the  coil.    Two  forces 
are  now  acting  on   the   needle  and  balancing   each  other,  viz.,  the 
directive  force  of  the  earth's  magnetism,  and  the  deflecting  force  of 
the  current  flowing  through  the  coil.     At  this  moment,  the  strength  of 
the  current  is  proportional  to  the  sine  of  the  angle  through  which  the  coil 
has  been  turned.     The  values  of  the  sines  may  be  obtained  from  a 
table  of  natural  sines.     Such  a  table  is  given  in  the  appendix. 

(d)  The  mirror  galvanometer  (Fig.  391)   has  a  very  short  needle 
rigidly  attached  to  a  small  concave  mirror  that  is  suspended  by  a 
delicate  fiber  in  the  center  of  a  vertical  coil  of  small  diameter.     A 
curved  magnet,  carried  on  a  vertical  support  above  the  coil,  serves  to 
counteract  the  earth's  magnetism,  and  to  bring  the  needle  into  the 
plane  of  the  coil  when  the  latter  does  not  coincide  with  the  magnetic 
meridian,  or  to  direct  it  within  the  coil.     A  beam  of  light  from  a 
lamp  passes  through  a  small  opening  under  a  millimeter  scale  about  a 
meter  from  the  mirror,  falls  upon  the  mirror,  and  is  reflected  back 
upon  the  scale.     The  curved  magnet  enables  the  operator  to  bring  the 
spot  of  refle6ted  light  to  the  zero  mark  at  the  middle  of  the  scale.     A 
current  passing  through  the  coil  turns  the  needle  and  its  mirror,  thus 
shifting  the  spot  of  light  to  the  right  or  left  of  the  zero  point.     The 
current  through  the  galvanometer  may  be  reduced  by  shunt  to  any 
desirable  extent,  thus  extending  the  serviceable  range  of  the  instru- 
ment.     The  apparatus  was  devised  by  Sir  William  Thomson,  now 


ELECTRICAL   MEASUREMENTS.  527 

Lord  Kelvin,  for  use  in  connection  with  the  Atlantic  cablo,  and  is 
exceedingly  sensitive.  The  current  produced  by  dipping  the  point  of 
a  brass  pin  and  the  point  of  a  steel  needle  into  a  drop  of  salt  water, 
and  closing  the  external  circuit  through  this  instrument  sends  the 
spot  of  light  swinging  way  across  the  scale. 

(e)  In  the  Deprez-d'Arsonval  dead-beat  reflecting  galvanometer,  a 
movable  coil  is  suspended  between  the  poles  of  a  strong,  permanent 
U-magnet  that  is  fixed.  The  coil  consists 
of  many  turns  of  fine  wire  the  terminals  of 
which  above  and  below  serve  as  the  sup- 
porting axis.  Within  the  coil  is  an  iron 
tube  that  is  supported  from  the  back,  and 
that  serves  to  concentrate  the  magnetic 
field.  The  passage  of  a  current  turns  the 
coil,  and  sets  it  so  that  its  plane  encloses 
a  larger  number  of  lines  of  force.  This 
movement  of  the  coil  turns  the  mirror  by 
means  of  which  the  angles  of  deflection  are 

read  with  a  telescope  and  scale.     When  the 

,  .,    ,    ,,  .„  FIG.  418. 

galvanometer  is  short  circuited,  the  oscilla- 
tions of  the  coil  induce  currents  that  quickly  bring  it  to  rest.     It  is 
simple  in  construction,  and  almost  wholly  independent  of  the  mag- 
netic field  surrounding  it. 

(/)  In  the  differential  galvanometer,  the  coil  is  made  of  two  sepa- 
rate wires  wound  side  by  side.  If  two  equal  currents  are  sent  through 
these  wires  in  opposite  directions,  the  needle  will  not  be  deflected.  If 
the  currents  are  unequal,  the  needle  will  be  deflected  by  the  stronger 
one  with  a  force  corresponding  to  the  difference  of  the  strengths  of 
the  two  currents.  It  is  much  used  in  null  methods  of  measurement. 

(</)  The  ballistic  galvanometer  is  provided  with  a  heavy  needle  that 
has  a  slow  rate  of  oscillation,  and  that  k  strongly  magnetized  and 
placed  in  a  strong  directing  field.  It  is  used  for  measuring  currents 
that  are  variable  in  the  time  of  measurement,  and  in  measuring 
condenser  capacity.  The  discharge  causes  the  needle  to  give  a  sudden 
kick.  The  quantity  of  electrification  discharged  and  the  capacity  of  the 
condenser  are  respectively  proportional  to  the  sine  of  half  the  angle  of 
deflection  of  the  needle. 

(h)  A  galvanometer  of  low  resistance,  empirically  calibrated,  i.e., 
graduated  for  the  direct  measurement  of  electric  currents  and  giving 
its  readings  in  amperes,  is  called  an  ammeter,  or  ampere-meter.  Any 


528 


SCHOOL   PHYSICS. 


FIG.  419. 


galvanometer  that  is  wound  with  wire  of  sufficient  size  safely  to  carry 

the  current  to  be  measured, 
and  properly  calibrated, 
may  be  used  as  an  amme- 
ter. Fig.  419  shows  one  of 
the  common  forms  in  prac- 
tical use. 

(i)  An  electrodynamom- 
eter  is  a  galvanometer  with 
two  coils,  at  least  one  of 
which  is  movable,  and 
through  at  least  one  of 
which  the  current  to  be 
measured  passes.  It  is  very 
useful  in  the  measurement 
of  alternating  currents  and  voltages.  Fig.  420  shows  a  form  of  the 
instrument  that  is  much  used  in  practice.  The  torque  of  the  movable 
coil  is  resisted  by  a  spiral 
spring.  The  deflection  caused 
by  the  current  is  indicated  on 
a  properly  graduated  dial,  and 
from  such  indications  the  cur- 
rent or  voltage  is  computed. 
Such  an  instrument  calibrated 
for  direct  currents  measures 
the  square  root  of  mean  square 
values  of  alternating  currents. 
(/)  If  a  galvanometer  is 
put  in  shunt  circuit  between 
two  points  of  different  poten- 
tials, current  will  pass  through 
it,  and  the  current  thus  pass- 
ing may  be  used  to  measure 
the  difference  of  potential.  A 
galvanometer  of  high  resist- 
ance, calibrated  so  as  to  indi- 
cate in  volts  the  difference  of  pIG  420 
potential  between  its  termi- 
nals, is  called  a  volt-meter.  The  resistance  must  be  high  so  as  to  reduce 
the  shunted  current,  for,  if  the  shunted  current  is  large,  the  difference 


ELECTRICAL   MEASUREMENTS. 


529 


of  potential  between  the  terminals  will  be  lowered,  a  change  of  the 
very  function  that  is  to  be  measured.  In  general,  a  volt-meter  is  a 
galvanometer  properly  calibrated,  and  wound  so  as  to  have  a  resist- 
ance of  from  5,000  to  50,000  ohms. 

(fc)  If  the  movable  coil  of  an  electrodynamometer  is  made  of  very 
fine  wire  suitable  for  voltage  measurement,  and  the  stationary  coil  of 
coarse  wire  suitable  for  current  measurement,  and  the  high-resistance 
coil  is  put  in  parallel  with  the  main  circuit,  and  the  low-resistance 
coil  is  put  in  series,  the  apparatus  may  be  used  to  measure,  in  watts, 
the  rate  of  working,  or  the  electrical  activity  of  the  current.  Such  a 
device  is  called  a  wattmeter. 

(/)  Electric  current  being  a  merchantable  commodity,  it  is  often 
desirable  to  measure  both  the  rate  at  which  the  electrical  energy  is 
delivered  and  the  time  that  it 
is  delivered,  i.e.,  the  number 
of  watt-hours.  This  is  accom- 
plished by  a  modification  of 
the  wattmeter.  The  current 
swings  an  armature  coil  with 
complete  revolutions  in  the 
field  of  a  stationary  coil. 
These  revolutions  are  counted 
by  a  registering  apparatus  that 
gives  direct  readings  in  watt- 
hours.  The  tendency  of  the 
armature  to  turn  is  directly 
proportional  to  the  current. 
The  rotary  motion  of  the  ar- 
mature is  retarded  by  a  copper  FIG.  421. 
disk  that  revolves  between 

magnet  poles  as  shown  in  Fig.  421.  The  motion  of  the  disk-conductor 
in  the  magnetic  field  develops  in  the  disk  eddy  or  local  currents  that 
produce  the  required  drag  or  brake  on  the  revolving  armature. 

(TO)  The  resistance  of  a  galvanometer  should  correspond  to  that 
of  the  rest  of  the  circuit ;  i.e.,  a  high  resistance  galvanometer  should 
be  used  on  a  high  resistance  circuit,  and  vice  versa. 


415.    Resistance  Coils  are  made  of  wires  of  known  resist- 
ance for  use  with  galvanometers  in  measuring  resistances. 
34 


530 


SCHOOL   PHYSICS. 


FIG.  422. 


Insulated  and  doubled  wires  are  wound  upon  spools,  and  the 

terminals  of  each  spool  con- 
nected to  heavy  brass  blocks, 
A)  B,  C,  etc.,  on  the  top  of  the 
box  that  carries  the  spools. 
This  style  of  winding  destroys 
the  magnetic  effects,  and  re- 
duces the  self-induction  of  the 
coils.  When  the  brass  plugs 
are  inserted,  as  shown  in  Fig.  422,  the  coils  are  short- 
circuited,  i.e.,  practically,  the  whole  of  a  current  passing 
from  block  to  block 
goes  through  the 
plug,  but  when  a 
plug  is  withdrawn 
the  current  passes 
through  the  corre- 
sponding coil.  Such 
coils  with  resist- 
ances of  1,  2,  2,  5, 
10,  10,  20,  50,  100,  100,  200,  500  ohms,  etc.,  severally  are 
connected  to  form  a  resistance-box  as  shown  in  Fig.  423. 
By  withdrawing  the  proper  plugs,  one  may  throw  into 
the  circuit  any  resistance  desired,  from  a  single  ohm  up 
to  the  full  capacity  of  the  box. 

(a)  Formerly,  German-silver  wire  was  generally  used  for  resistance 
coils  because  its  resistance  is  high  and  little  influenced  by  temperature. 
"Platinoid"  wire,  an  alloy  of  German-silver  and  tungsten,  is  now 
generally  used  for  this  purpose,  as  it  is  much  harder,  has  a  much 
higher  specific  resistance,  and  a  lower  temperature  coefficient,  and  is 
not  expensive. 


FIG.  423. 


ELECTRICAL   MEASUREMENTS. 


531 


416.  The  Measurement  of  Resistance  is  done  in  several 
ways  according  to  the  nature  and  magnitude  of  the  resist- 
ance. Much  use  is  made  of  the  following  important 
principle :  The  fall  of  potential  betiveen  two  points  on  a 
conductor  is  proportional  to  the  resistance  of  the  conductor 
between  those  points. 

(«)  In  Experiment  305,  we  observed  a  certain  deflection  of  the 
galvanoscope  with  a  wire  of  unknown  resistance  in  the  circuit.  By 
removing  such  an  unknown  resistance,  and  inserting  known  resist- 
ances until  the  same  deflection  of  the  same  galvanoscope  with  the 
same  cell  is  obtained,  we  may  determine  the  resistance  of  the  wire 
first  used.  This  method  is  called  resistance  measurement  by  substitu- 
tion. Its  chief  defect  arises  from  the  variation  in  the  power  of  the 
cell. 

(&)  The  method  explained  above  may  be  used  with  any  galvanom- 
eter of  sufficient  sensitiveness,  but 
with  a  tangent  galvanometer,  the  proc- 
ess may  be  shortened.  Suppose  the 
tangent  galvanometer  and  an  un- 
known resistance,  R,  to  be  included 
in  the  circuit,  as  in  Fig.  424,  and  that 
the  deflection  is  a  degrees.  Substitute 
for  R  any  known  resistance,  r,  which 
gives  a  deflection  of  b  degrees.  Since 
the  strengths  of  the  currents  are  proportional  to  tan  a  and  tan  b 
respectively,  the  resistance,  R,  may  be  calculated  by  the  inverse  pro- 
portion : 

tan  a  :  tan  b  :  :  r:  R. 

(c)  Another  method  is  to  divide  the  circuit  into  two  branches  so 
that  a  part  of  the  current  flows  through  the  given  resistance  and  round 
one  set  of  coils  of  a  differential  galvanometer,  the  other  part  of  the 
current  bejng  made  to  flow  through  known  resistances  and  then  round 
the  other  set  of  coils  in  the  opposing  direction.  When  we  have 
matched  the  unknown  resistance  by  an  equal  known  resistance,  the 
currents  in  the  two  branches  will  be  equal,  and  the  needle  of  the 
differential  galvanometer  will  show  no  deflection.  With  an  accurate 
instrument,  this  method  is  very  reliable.  When  the  instrument  is  not 


Fm.  42 


532 


SCHOOL  PHYSICS. 


known  to  be  accurate,  a  better  way  is  to  balance  the  given  resistance 
with  other  resistances,  known  or  unknown.  Then  substitute  known 
resistances  for  the  given  resistance  until  the  deflection  of  the  galva- 
nometer again  is  nil.  Compare  §  132  (&), 

(cT)  The  method  that  has  the  most  general  application  is  that  known 
as  the   Wheatstone  bridge.      In   Fig.  425,  we  have  a  quadrangle   of 


FIG.  425. 

resistances.  The  four  conductors,  m,  n,  p,  and  x,  that  form  the  sides 
are  called  the  "arms;"  the  conductor  that  joins  C  and  D  and  carries 
the  galvanometer,  G,  is  called  the  "bridge."  The  current  divides 
at  Ay  and  reunites  at  B.  The  fall  of  potential  through  n  and  x  is 
evidently  the  same  as  the  fall  through  m  and  p.  The  resistances  of 
the  arms  may  be  so  adjusted  that,  when  the  bridge-circuit  is  closed 
at  K,  there  will  be  no  deflection  of  the  needle  of  G.  Under  such  cir- 
cumstances, C  and  D  are  at  the  same  potential,  and  it  may  be  shown 
that  the  resistances  of  the  four  arms  "  balance  "  by  being  in  propor- 
tion, thus :  — 

m  :  n  : :  p  :  x. 

When  three  of  these  resistances  are  known,  the  other  one  may  be  cal- 
culated, or  if  the  ratio  of  m  :  n,  and  the  value  of  p  are  known,  the 


ELECTRICAL   MEASUREMENTS. 


533 


value  of  x  may  also  be  determined.     Under  the  conditions  described, 
it  is  also  true  that  m  :  p  : :  n  :  x. 

The  practical  working  of  this  method  may  be  illustrated  as  fol- 
lows :  Suppose  that  x  is  the  resistance  to  be  determined.  The  other 
three  arms  are  built  up  from  the  coils  of  a  standard  resistance-box. 
The  arms,  m  and  n,  are  called  the  "  balance-arms,"  and  are  so  cut  into 
the  circuit  by  the  removal  of  plugs  that  the  ratio  between  their  resist- 
ances is  decimal,  as  10  or  100,  thus  simplifying  the  solution  of  the 
proportion.  To  illustrate,  suppose  that  the  resistance  of  m  is  10  ohms ; 
that  of  n,  100  ohms ;  and  that  of  jo,  15  ohms,  as  represented  by  Fig. 


FIG.  426. 

426.  Then  the  resistance  of  a;  is  150  ohms.  If  the  resistance  of  n  is 
10  ohms ;  that  of  /«,  100  ohms,  and  that  of  p,  464  ohms,  the  resistance 
of  x  is  46.4  ohms.  In  using  the  bridge,  the  battery  circuit  should 
always  be  made  by  depressing  the  key,  £,  before  K.  the  key  of  the 
galvanometer  branch,  is  depressed.  This  avoids  the  sudden  "throw" 
of  the  galvanometer  needle,  in  consequence  of  self-induction,  when 
the  circuit  is  closed. 

417.  The  Measurement  of  Internal  Resistance.  —  The 
best  way  of  determining  the  internal  resistance  of  a  vol- 
taic cell  is  to  join  two  similar  cells  in  opposition  to  one 
another,  so  that  they  send  no  current  of  their  own.  Then 


534  SCHOOL   PHYSICS. 

measure  their  united  resistance  (as  if  it  were  the  resist- 
ance of  a  wire)  as  just  described.  The  resistance  of  one 
cell  will  be  half  that  of  the  two. 

418.  The  Measurement  of  E.M.F.,  or  of  difference  of 
potential,   is   generally   made   with  a  volt-meter,    or    by 
comparison  with  the  E.M.F.  of  a  standard  cell. 

(a)  Represent  the  known  E.M.F.  of  a  Daniell  cell  by  E,  and  that 
of  the  given  cell  or  battery  by  x.  Connect  the  given  cell  to  the  gal- 
vanometer, and  note  the  number  of  degrees  of  deflection  that  it  pro- 
duces. Represent  this  deflection  by  a.  Then  add  enough  resistance, 
R,  to  bring  the  deflection  down  to  b  degrees  (e.g.,  10  degrees  less 
than  before).  Then  substitute  the  Daniell  for  the  given  cell  in  the 
circuit,  and  adjust  the  resistances  of  the  circuit  until  the  galvanometer 
shows  a  deflection  of  a  degrees,  as  at  first.  Add  enough  resistance,  r, 
to  bring  the  deflection  down  to  b  degrees  as  before.  E,  R  and  r  being 
known,  x  may  be  found  from  the  proportion, 

r:R::E:x, 

because  the  resistances  that  produce  an  equal  reduction  of  current  are 
proportional  to  the  electromotive  forces. 

419.  The  Measurement  of  the  Capacity  of  a  condenser 
is  accomplished  by  placing  the  given  condenser,  K,  a  stand- 
ard condenser,  K',  and  known  resistances,  r  and  r\  in  the 
arms  of  a  Wheatstone  bridge,  as  shown  in  Fig.  427. 

(a)  By  pressing  the  key  on  the  stop,  a,  the  current  flows  through 
the  point,  B,  and  charges  the  condensers,  the  greater  quantity  going 
to  the  condenser  of  greater  capacity.  The  resistances,  r  and  r',  are 
adjusted  so  that  there  is  no  deflection  of  the  needle  at  G.  When  the 
key  is  pressed  on  the  other  stop,  c,  there  is  a  rush  of  current  from  the 
condensers  that  is  retarded  by  the  resistances,  r  and  r'.  Any  change 
or  inequality  of  the  voltage  of  the  condensers  is  instantly  shown  by 
the  galvanoscope.  Assuming  that  the  capacity  of  K  is  less  than  that 
of  K',  its  voltage  will  fall  more  rapidly  unless  the  resistance,  r,  is 
greater  than  r'.  Since  capacity  equals  quantity  divided  by  potential, 

*->' 


ELECTRICAL   MEASUREMENTS. 


535 


it  follows  that  if  the  resistances  are  adjusted  so  that  the  voltages  are 
the  same  for  both  (i.e.,  no  deflection  at  G)  K  will  be  directly  propor- 
tional to  Q.  As  the  condensers  discharge  in  the  same  time,  their 


FIG.  427. 

capacities  are  proportional  to  the  currents  sent  through  r  and  rf.  As 
these  currents  have  the  same  E.M.F.,  each  is  inversely  proportional  to 
the  resistances  through  which  it  flows.  Hence 

K  :  K'  :  :  r'  :  r. 
Three  of  these  values  being  known,  K  is  easily  determined. 

420.  The  Measurement  of  Magnetic  Functions.  —  Mag- 
netic flux  is  measured  directly  in  webers  by  the  use  of  a 
little  exploring  coil  of  many  turns  of  fine  wire  connected 
to  a  ballistic  galvanometer.  The  quantity  of  the  current 


536  SCHOOL   PHYSICS. 

generated  by  suddenly  jerking  the  exploring  coil  from  the 
magnetic  field  is  thus  measured,  and  from  this  the  number 
of  lines  of  force  is  calculated.  Magnetomotive  force  is 
usually  calculated  directly  from  the  ampere-turns.  Mag- 
netizing force  is  calculated  by  dividing  the  magnetomotive 
force  by  the  length  of  the  magnetic  circuit  in  centimeters. 
Permeability  is  calculated  directly  from  the  quotient  of  the 
induction  and  the  magnetizing  force.  Curves  of  per- 
meability may  be  determined  for  iron  at  various  stages  of 
magnetization,  and  each  kind  of  iron  nas  its  own  curve. 
Such  curves  are  largely  used  in  dynamo  design. 

CLASSROOM  EXERCISES. 

/ 

1.  Draw  an  illustrative  diagram,  and  deduce  the  formula  for  the 
Wheatstone  bridge. 

2.  Explain  why  an  ammeter  should  have  a  low  resistance,  and  a 
volt-meter  a  high  resistance. 

3.  A  volt-meter  that  has  a  resistance  of  26,000  ohms  indicates  37 
volts,     (a)  What  is  the  strength  of  the  current  ?     (ft)  What  voltage 
would  such  an  instrument  indicate  with  a  current  of  3  milliamperes  ? 

4.  Two  volt-meters,  one  of  which  has  a  resistance  of  25,000  ohms, 
and  the  other  a  resistance  of  15,000  ohms,  are  connected  in  series 
across   110  volts.      (a)  What  current  flows   through    the    system? 
(ft)  What  voltage  does  the  first  instrument  indicate?   (c)  the  second 
instrument  ? 

Ans.  (a)  0.00275  amperes;  (ft)  68.75  volts;  (c)  41.25  volts. 

5.  I  have  a  volt-meter  that  measures  up  to  15  volts  and  that  has  a 
resistance  of  3,500  ohms.     I  want  to  use  it  on  a  115-volt  circuit,  and, 
therefore,  put  it  in  series  with  a  resistance  of  24,000  ohms.    With  the 
two  thus  connected,  and  with  a  voltage  of  110,  (a)  What  is  the  current 
strength?      (ft)  What  is  the  indication  of  the  volt-meter?      (c)  By 
what  must  the  reading  of  the  volt-meter  be   multiplied   to  get  the 
actual  voltage  ?    Suppose  the  voltage  to  be  increased  to  1 17.    (d)  What 
is  the  reading  of  the  volt-meter?      (e)  Is  there  any  change  in  the 
multiplier  used  to  give  the  correct  voltage  ? 


ELECTRICAL   MEASUREMENTS.  537 

6.  "What  resistance  must  be  put  in  series  with  the  volt-meter  of 
Exercise  5,  so  that  the  multiplier  shall  be  10?          Ans.  31,500  ohms. 

7.  How  many  watts  is  taken  by  a  station  volt-meter  that  indicates 
110  volts  and  uses  a  0.002-ampere  current? 

8.  I  have  an  ammeter  that  indicates  milliamperes  up  to  100.    It  has 
a  resistance  of  6  ohms.     I  desire  to  put  it  on  a  circuit  that  I  know  to 
have  a  current  of  6  or  7  amperes.     As  the  instrument  will  not  safely 
carry  more  than  0.1  of  an  ampere,  I  put  it  in  a  shunt,  as  shown  in  Fig. 
432.     What  must  be  the  resistance  of  R,  the  other  branch  of  the  cir- 
cuit, so  that  the  instrument  shall  have  a  multiplier  of  100 ;  i.e.,  so  that 
a  current  of  6.5  amperes  will  produce  a  reading  of  65  milliamperes  ? 
Evidently,  with  such  a  current  and  with  the  shunts  properly  adjusted, 
0.065  of  an  ampere  will  pass  through  the  milliammeter,  and  6.435 
amperes  through  R. 

9.  At  an  electric  light  station,  I  am  called  upon  to  measure  the 
resistance  of  one  of  the  field-magnet  coils  of  a  dynamo.     I  have  a  volt- 
meter and  an  ammeter,  and  a  small  dynamo  (the  exciter  of  an  alter- 
nator) that  will  furnish  a  15-ampere  current  at  any  desired  voltage 
from  150  to  225.     With  this  outfit,  how  shall  I  measure  the  resistance 
of  the  coil  ? 

10.  Draw  a  sketch  of  the  connections  of  a  series  dynamo,  and  show 
how  you  would  arrange  a  volt-meter  to  measure  the  voltage  necessary 
to  force  the  current  through  the  field  magnets. 


LABORATORY  EXERCISES. 

Additional  Apparatus,  etc.  —  Three  Danisll  cells ;  galvanoscopes  and 
galvanometers ;  volt-meter ;  ammeter ;  resistance-box  ;  rheochord  as 
described  below  ;  current  reverser ;  2m.  of  fine  platinum  wire ;  double 
connector ;  wires  of  unknown  resistance ;  Wheatstone  slide-bridge  as 
described  below. 

1.  Solder  one  end  of  a  piece  of  No.  20  insulated  copper  wire,  50  cm. 
long,  to  one  end  of  a  piece  of  zinc  10  x  2.5  x  0.5  cm.,  and  amalgamate 
the  zinc.  Solder  a  similar  wire  to  a  piece  of  sheet  copper  10  x  10  cm. 
Put  the  zinc  into  a  porous  cup  4  or  5  cm.  in  diameter  and  10  cm.  deep, 
and  fill  the  cup  to  the  depth  of  8  cm.  with  dilute  sulphuric  acid.  Put 
the  copper  plate  into  a  glass  vessel  7  or  8  cm.  in  diameter  and  10  cm. 
deep,  bending  it  slightly  to  fit  the  inner  surface  of  the  tumbler.  Put 
the  porous  cup  and  its  contents  into  the  glass  vessel,  and  fill  the  latter 
to  the  depth  of  8  cm.  with  a  saturated  solution  of  copper  sulphate. 


538 


SCHOOL  PHYSICS. 


Connect  the  terminals  of  this  Daniell  cell  with  the  terminals  of  a  low 
resistance  galvanoscope,  and  record,  at  intervals  of  5  minutes  for  half 
an  hour,  the  deflections  of  the  needle.  Ascertain  whether  the  current 
strength  is  practically  constant  after  the  porous  cup  is  wet  through. 

2.  Make  a  resistance  frame  (rheochord)  as  follows:  Nail  two 
uprights,  each  25  x  3  x  1  cm.  to  the  edge  of  a  plank  100  x  10  x  4  cm., 
and  screw  the  ends  of  a  meter  stick  to  the  upper  ends  of  the  uprights, 
as  shown  in  Fig.  428.  Set  two  small  metal  binding-posts  at  a,  and 
another  pair  at  the  same  level  at  6.  Set  similar  binding-posts,  in 
pairs,  at  c,  d,  and  e.  Connect  the  base  of  the  inner  post  at  a  with  the 
base  of  the  inner  post  at  b  by  No.  30  German-silver  wire.  It  is  well 
to  solder  the  wire  to  the  posts.  Lead  a  similar  wire  around  the  outer 
edges  of  the  uprights,  and  connect  its  ends  to  the  outer  posts  at  a  and  b. 


FIG.  428. 


From  one  of  the  posts  at  c,  lead  a  similar  wire  around  both  uprights 
to  the  other  post  at  c.  In  like  manner,  connect  the  posts  at  d  by  No. 
28  German-silver  wire.  In  like  manner,  connect  the  posts  at  e  by  10 
turns  of  insulated  No.  30  copper  wire,  laying  the  wire  on  carefully  so 
as  to  prevent  the  current  from  leaking  across  from  one  turn  to  the 
next  (short-circuiting).  All  of  the  posts  should  be  firmly  fixed,  and 
the  wire  should  be  drawn  tight. 

Near  each  corner  of  a  wooden  block  about  10  cm.  square,  bore  a 
centimeter  hole,  about  a  centimeter 
deep,  and  number  the  holes  in  succes- 
sion, 1,  2,  3,  and  4.  These  holes  are 
for  mercury  cups.  Set  sharp  little  spikes 
at  the  corners  of  the  opposite  face  of  the 
block,  to  fix  it  to  the  table  wherever  it 
is  placed.  Set  metal  binding-posts  at 
FIG.  429.  the  corners  of  the  block  so  that  the 


ELECTRICAL  MEASUREMENTS.          539 

screw  of  each  penetrates  to  one  of  the  cups.  Provide  two  stout  copper 
wires,  amalgamated  at  their  ends,  and  bent  so  that  they  may  connect 
any  of  the  holes  with  either  of  the  two  adjoining  holes.  When  mer- 
cury is  placed  in  the  cups,  the  block  constitutes  a  "current  reverser" 
or  mercury  commutator. 

Connect  diagonally  opposite  mercury  cups  (as  1  and  3)  of  the  com- 
mutator to  the  terminals  of  a  Daniell  cell.  From  one  of  the  other  cups 
(as  2),  lead  a  wire  to  one  of  the  terminals  of  a  low  resistance  galvano- 
scope,  and  connect  the  other  terminal  of  the  galvanoscope  to  one  of 
the  binding-posts  (at  6)  of  the  rheochord.  From  the  other  binding- 
post  at  6,  lead  a  wire  to  the  fourth  mercury  cup.  The  galvano- 
scope should  be  at  least  a  meter  from  the  other  parts  of  the  apparatus 
so  that  its  needle  may  be  unaffected  by  them,  and  the  wires  leading 
to  and  from  it  should  lie  close  together.  Connect  the  two  binding- 
posts  at  a  by  a  short,  stout  copper  wire.  Complete  the  circuit  by 
placing  the  two  bent  copper  wires  so  that  one  of  them  shall  connect 
cups  2  and  3,  while  the  other  connects  1  and  4.  Trace  the  direction 
of  the  current  through  the  galvanoscope.  Change  the  bent  wires  of 
the  commutator  so  that  one  of  them  connects  1  and  2,  while  the  other 
connects  3  and  4.  Trace  the  direction  of  the  current  through  the 
commutator.  By  this  time,  the  porous  cup  of  the  cell  will  probably 
be  wet  through,  and  the  current  nearly  constant. 

While  the  current  is  flowing  through  200  cm.  of  No.  30  German- 
silver  wire,  record  the  deflection  of  the  needle  of  the  galvanoscope ; 
reverse  the  current  and  record  the  deflection ;  record  the  average  of 
the  two  deflections.  With  a  copper  wire  or  a  double  connector  like 
that  shown  in  Fig.  430,  short  circuit  the  two  wires  near  a,  so  that  the 
current  shall  flow  through  180  cm.  of  the  German-silver  wire.  Record 
the  three  deflections  as  before.  Make  similar  successive  records  for 
160,  140,  120,  100,  80,  and  60  cm.  of  the 
German-silver  wire,  ending  with  the  record 
for  200  cm.,  taken  again  to  be  sure  that 
the  current  has  not  fallen  off  while  the 
measurements  were  in  progress.  Tabulate  FIG.  430. 

all  of  your  records,  and  notice  whether  they  indicate,  in  a  general  way, 
any  dependence  of  electrical  resistance  upon  the  length  of  the 
conductor. 

3.  Using  the  apparatus  arranged  for  Exercise  2,  change  the  con- 
nections at  the  rheochord  from  b  to  d,  so  as  to  put  the  200  cm.  of  Xo. 
28  German-silver  wire  into  the  circuit.  Record  the  deflection  ;  reverse 


540  SCHOOL  PHYSICS. 

the  current,  and  record  the  deflection ;  and  record  the  average  of  the 
two  deflections.  Compare  this  average  with  the  averages  obtained  in 
Exercise  2  for  the  several  lengths  of  No.  30  wire,  and  estimate  the 
length  of  the  latter  that  has  a  resistance  equal  to  that  of  the  200  cm. 
of  No.  28  wire.  Carefully  measure  the  diameters  of  the  two  wires, 
and  compute  the  ratio  between  the  areas  of  their  cross-sections.  De- 
termine the  relation  between  cross-section  and  resistance. 

4.  Using  the  apparatus  arranged  for  Exercise  3,  change  the  con- 
nections from  d  to  c,  and   connect  the  two  binding-posts  at  b  by 
copper  wires  to  the  two  binding-posts  at  d,  so  as  to  provide  for  the 
current,  two  equal  parallel  branches  of  No.  30  German-silver  wire. 
Record  the  deflections  before  and  after  reversal,  and  their  average,  as 
before.     Estimate  the  length  of  No.  30  wire,  as  used  in  Exercise  2, 
that  has  a  resistance  equal  to  that  of  the  two  200-cm.  pieces  in  multi- 
ple arc  as  used  in  this  exercise. 

5.  Determine  the  length  of  No.  30  German-silver  wire  that  has  a 
resistance  equal  to  that  of  20  m.  of  No.  30  copper  wire. 

6.  Wind  into  spiral  coils  two  equal  lengths  (e.g.,  1QO  cm.)  of  fine 
platinum  wire,  and  put  them  into  the  arms  of  a  Wheatstone  bridge. 
Balance  the  bridge.     Heat  one  of  the  spirals  in  a  Bunsen  or  alcohol 
flame,  and  notice  that  the  deflection  of  the  needle  indicates  that  the 
balance  has  been  destroyed.     While  the  spiral  is  still  heated,  balance 
(roughly)  the  bridge  again,  and  determine  whether  the  resistance  of 
the  wire  was  increased  or  decreased  by  the  rise  of  temperature. 

7.  Place  in  the  circuit  of  the  Daniell  cell  of  Exercise  1,  a  galvano- 
meter, a  set  of  resistance  coils,  and  a  conductor,  X,  of  unknown  resist- 
ance.     Adjust  the  known  resistances  so  that  the  needle  shows    a 
deflection  of  about  45°,  and  record  the  exact  reading.     Remove  X 
from  the  circuit.     Add  known  resistances  to  make  the  deflection  the 
same  as  before.     Repeat  the  work  twice,  adjusting  the  known  resist- 
ances so  as  to  produce  deflections  of  about  43°  and  47°,  and  take  the 
average  of  the  three  totals  of  added  resistance  as  the  resistance  of  X. 
This  is  called  the  method  by  substitution. 

8.  To  a  table-top  or  other  board,  tack  two  stout  metal  strips,  AC 
and  BD,  with  a  meter-stick  between  them,  as  shown  in  Fig.  431. 
Tack  a  similar  metal  strip,  EF,  90  cm.  long,  in  position  as  shown. 
Solder  metal  binding-posts  at  the  ends  of  these  strips,  and  at  the 
middle  of  EF.     The  resistance  of  the  strips  is  negligible.     Tightly 
stretch  a  German-silver  wire,  No.  26,  over  the  face  of  the  meter  stick, 
and  solder  it  to  the  faces  of  the  metal  strips  at  r  and  s.     One  of  the 


ELECTRICAL   MEASUREMENTS. 


541 


terminals  of  a  sensitive  galvanoscope  is  to  be  connected  to  EF ';  the 
other  galvanoscope  wire  is  to  make  a  sliding  contact  with  the  Ger- 
man-silver wire,  dividing  it  into  two  variable  parts,  m  and  p.  Put  the 
apparatus  into  the  circuit  of  a  voltaic  cell,  as  shown  in  the  figure. 
Interpose  a  conductor  of  unknown  resistance  at  x  and  a  known  resist- 
ance of  approximately  the  same  value  at  n  (the  better  this  guess  at  the 
equality  of  resistances,  the  less  the  liability  of  error  in  the  results 
attained).  You  have  a  AYheatstone  bridge,  easily  comparable  to 


FIG.  431. 

that  shown  in  Fig.  425.  Make  the  sliding  contact  at  a  point  on  rs 
that  causes  a  deflection  to  the  right,  and  note  its  position  on  the 
meter-scale ;  find  a  position  that  causes  a  deflection  to  the  left.  As 
the  point  of  contact  at  which  the  bridge  will  balance  is  between  these 
points,  it  is  easy  to  locate  it  definitely.  When  the  contact  is  made  at 
such  a  point  on  rs  that  there  is  no  deflection  of  the  needle,  read  the 
values  of  m  and  p,  directly  from  the  meter-scale,  and  determine  the 
resistance  of  x.  Repeat  the  work  with  two  slightly  different  values 
for  n,  and  take  the  average  of  the  three  computed  values  of  x. 

Note.  —  In  practice,  the  galvanoscope  should  be  placed  at  a  distance 
from  the  rest  of  the  apparatus,  the  connecting  wires  being  kept  near 
together. 

9.  Make  a  Daniell  cell  similar  to  that  of  Exercise  1,  with  cups  of 
the  same  size  but  with  plates  of  sheet  metal  and  10  x  0.5  cm.  in  size. 
Take  care  that  the  liquids  are  of  the  same  depth  in  the  two  cells. 
Put  the  large-plate  cell  in  circuit  with  a  galvanoscope,  inserting  the 
commutator  as  in  some  of  the  preceding  exercises.  Set  the  plates  as 


542  SCHOOL   PHYSICS. 

far  apart  as  possible,  and  record  the  deflections  before  and  after 
reversal,  and  their  average.  Repeat  the  work  with  the  plates  as  near 
together  as  possible.  Repeat  both  tests  with  the  small-plate  cell. 
Put  200  cm.  of  No.  30  German-silver  wire  into  the  circuit,  and  repeat 
the  work  with  the  two  cells  in  succession.  Repeat  these  latter  tests, 
using  a  galvanoscope  of  higher  resistance.  From  your  record,  deter- 
mine the  effect  of  the  size  of  the  plates,  and  of  the  distance  between 
the  plates  upon  the  current  strength,  and  whether  the  addition  of  an 
external  resistance  has  any  effect  upon  the  sensitiveness  of  the  current 
to  changes  in  the  size  and  relative  positions  of  the  plates. 

10.  Replace  the  small  plates  of  the  cell  described  in  Exercise  9  by 
plates  like  those  of  the  cell  of  Exercise  1.     Join  the  two  like  cells  in 
parallel,  and  put  into  the  circuit  a  galvanoscope,  and  200  cm.  of  No. 
30  German-silver  wire.     Record  the  deflections  as  previously  directed. 
Make  the  tests  with  galvanoscopes  of  high  and  of  low  resistances. 
Repeat  the  tests  with  the  cells  joined  in  series.    Remove  the  German- 
silver  wire  from  the  circuit,  and  repeat  the  tests.     From  your  record, 
determine  under  what  conditions  it  is  better  to  join  cells  in  pafallel, 
and  when  it  is  better  to  join  them  in  series. 

11.  Join  the  two  Daniell  cells  of  Exercise  10  in  parallel,  and  sub- 
stitute the   battery  for  the  unknown   resistance,  x,  of  Exercise  8. 
Remove  the  battery  used  in  that  exercise,  or  leave  it  open  circuited 
at  k  (Fig.  426).     Compare  the  resistance  of  the  battery  with  that  of 
the  same  cells  in  series,  and  with  that  of  one  of  the  cells. 

Note.  —  The  accurate  measurement  of  the  resistance  of  a  cell  on 
closed  circuit  is  a  difficult  problem. 

12.  Place  a  volt-meter  that  indicates  tenths  of  a  volt  in  a  shunt 
circuit  around  a  resistance,  R,  as  shown  in  Fig.  432.    Assume  that  the 

resistance  of  the  instru- 
ment is  so  high  that 
the  current  shunted 
through  it  is  negligible. 
Determine  by  computa- 
tion  the  resistance  of  R 

— ->\A        A/VV\/VV\A* when    a   2-ampere  cur- 

Fl     432  ren*  flowing  through  it 

gives  a  reading  of  0.2 

at  the  volt-meter.  Try  to  verify  your  result  experimentally.  Notice 
that  the  readings  of  the  volt-meter  multiplied  by  10  give  the  current 


SOME   APPLICATIONS  OF  ELECTRICITY. 

strength  in  amperes.  Determine  the  value  that  should  be  given  to 
R  so  that  the  volt-meter  may  be  used  as  an  ammeter  giving  direct 
readings  in  amperes. 

Note.  — Many  ammeters  are  made  on  this  principle  of  shunning  a 
high  resistance  galvanometer. 


IV.    SOME  APPLICATIONS  OF  ELECTRICITY. 

Incandescence  Lighting. 

Experiment  382.  —  Place  a  few  centimeters  of  No.  36  platinum  wire 
across  the  terminals  of  a  battery  of  several  bichromate  cells  in  series. 
The  wire  will  be  heated  to  incandescence,  and  may  be  melted.  Lift 
one  of  the  plates  partly  from  the  liquid,  and  notice  the  diminished 
brilliancy  of  the  light  emitted  by  the  incandescent  wire.  By  gradu- 
ally lowering  the  plate  into  the  liquid  as  the  cells  weaken,  the  bril- 
liancy of  the  platinum  wire  may  be  kept  nearly  uniform.  Notice  the 
progressive  oxidation  of  the  wire.  Try  to  continue  the  experiment 
until  the  wire  breaks  down  by  oxidation,  noting  the  length  of  time 
taken.  Repeat  the  work  with  No.  36  iron  wire,  and  compare  the 
lasting  qualities  of  the  two  wires. 

421 .  Incandescence  Lamps  operate  essentially  on  the  prin- 
ciple illustrated  in  Experiment  382,  the  current  being  sent 
through  some  substance  thaf,  because  of  its 
high  resistance,  becomes  intensely  heated  and 
brilliantly  incandescent.  The  only  suitable 
substance  known  for  such  a  resistance  fila- 
ment is  carbon,  which,  carefully  prepared 
and  bent  into  a  loop,  is  enclosed  in  a  glass 
bulb  from  which  the  air  is  exhausted  to 
prevent  oxidation,  i.e.,  combustion.  At  the 
best,  the  filament  gradually  deteriorates  and 
finally  breaks,  thus  ruining  the  lamp.  The 
ends  of  the  carbon  filament  are  cemented  to  short  plati- 


544 


SCHOOL  PHYSICS. 


num  leading-in  wires  that  are  imbedded  in  the  glass  by 
the  fusion  of  the  latter.  These  platinum  wires  are  con- 
nected to  the  metallic  fittings  of  the  lamp  in  such  a  way 
that,  when  the  bulb  is  screwed  into  its  supporting  socket, 
the  connections  are  properly  made.  Some  such  lamps  are 
provided  with  turn-offs,  for  open-circuiting  the  lamp. 

(a)  As  incandescence  lamps  are  generally  connected  in  parallel,  as 
shown  in  Fig.  43-1,  they  require  a  heavy  current  at  a  comparatively 


1_J 1 


MAIN  SWITCH 


FIG.  434. 


low  voltage.  Such  currents  require  large  conductors  that  are  gener- 
ally made  of  copper.  The  "hot"  resistance  of  the  carbon  filaments 
Caries  from  about  25  to  250  ohms,  according  to  the  voltage  of  the  cur- 
rent and  the  candle-power  of  the  lamp.  In  what  is  known  as  "  the 
Edison"  3-wire  system,"  two  dynamos  are  connected  in  series,  as  shown 
in  Fig.  435.  The  lamps  on  each  side  of  the  middle  or  neutral  wire, 


SOME  APPLICATIONS   OF  ELECTRICITY. 


545 


vnr 


N,  are  made  as  nearly  equal  as  possible  in  number  and  resistance. 
When  they  thus  balance,  N  carries  no  cur- 
rent, and  the  voltage  of  the  second  dynamo  is 
added  to  that  of  the  first.  Under  such  con- 
ditions, the  effect  is  the  same  as  if  the  lamps 
of  each  pair  were  in  series,  the  doubled  re- 
sistance being  met  by  the  doubled  potential 
difference  of  the  two  generators.  Doubling 
thus  the  voltage  doubles  the  current,  and 
quadruples  the  energy  delivered.  This  en- 
ables a  division  of  the  area  of  cross-section  of 
the  line-wires  by  4,  and  results  in  a  saving 
of  f  of  the  weight  and  cost  of  the  mains.  If 
lamps  are  turned  out  on  one  side  of  the  mid- 
dle main,  current  flows  along  N  to  supply 
the  required  excess. 


Note.  —  The   arches   at  points  where  con- 
ductors cross  each  other  in  Fig.  434  indicate,  FIG.  435. 
in  the  conventional  way,  that  the  wires  cross 

without  contact.      Dynamos  are  often  represented  by  commutator 
circles  and  brushes  as  shown  in  Fig.  435. 

(ft)  With  lamps  placed  in  parallel,  the  greater  the  number  of  the 
lamps  in  use,  the  less  the  resistance  of  the  circuit.  The  current  is 
usually  operated  at  110  volts,  and  each  16-c.p.  lamp  takes  about  0.5  of 
an  ampere.  The  expenditure  is,  therefore,  nearly  3.5  watts  per 
candle-power.  Evidently,  an  increase  of  current  will  increase  the 
number  of  watts  expended  in  the  lamp,  and  the  quantity  of  light  pro- 
duced. The  greater  the  number  of  watts  expended,  the  higher  the 
temperature  of  the  filament,  and  the  greater  the  efficiency  of  the  lamp. 
But  excessive  temperatures  weaken  the  filament  and  shorten  its  time 
of  service,  so  that  in  practice  efficiency  is  sacrificed  to  some  extent  for 
the  sake  of  a  greater  durability. 

(c)  The  dynamos  designed  for  direct  use  with  such  lamps  are  gen- 
erally shunt-  or  compound-wound.  As  they  must  deliver  currents  that 
are  of  constant  potential  but  of  strength  that  varies  with  the  number 
of  lamps  in  use,  some  regulating  device  is  necessary  for  the  shunt- 
wound  dynamo ;  the  compound-wound  dynamo  is  self-regulating. 

(rf)  Incandescence  lamps  are  often  placed  on  the  secondary  circuit 
of  a  "  step  down  "  transformer,  the  primary  cirquit  of  which  carries 
36 


546 


SCHOOL   PHYSICS. 


the  high-voltage  current  of  an  alternator.  The  primary  coils  of 
several  transformers  may  be  put  in  series,  as  shown  in  Fig.  436,  or  in 
multiple  arc,  as  shown  in  Fig.  437. 


MAIN 


TO  THE  ALTERNATOR 


FIG.  436. 


(e)  When  electric  lamps  are  supplied  by  an  electric  lighting  com- 
pany, the  customer  sometimes  pays  a  fixed  rental  per  lamp  per  day. 


MAIN 
TO  THE  ALTERNATOR 

MAIN 


FIG.  437. 

and  sometimes  a  certain  price  per  watt-hour  for  the  current  actually 
delivered.  For  this  purpose,  a  wattmeter,  like  that  described  in 
§  414  (/),  is  often  used ;  the  Edison  meter  depends  upon  the  electro- 
lytic action  of  a  part  of  the  current  that  is  shunted  for  that  purpose. 
See  §  429  (a). 

Caution.  —  In  experimenting  with  an  incandescence  electric  lighting 
current,  remember  that  a  low  resistance  placed  across  the  mains  will 


SOME   APPLICATIONS   OF  ELECTRICITY.  547 

receive  an  enormous  current.  Many  a  galvanoscope  and  other  piece  of 
apparatus  has  been  ruined  in  this  way.  Never  "ground"  an  electric 
lighting  wire. 

The  Electric  Arc. 

Experiment  383.  —  Connect  one  of  the  terminals  of  the  battery  to  a 
small  file,  and  draw  the  other  terminal 
along  the  rough  surface.  A  series  of 
minute  sparks  is  produced  as  the  circuit 
is  rapidly  made  and  broken.  When 
such  a  luminous  effect  is  larger  and 
more  lasting,  the  band  of  light  between 
the  terminals  is  called  an  electric  arc. 

F  IG.    4oO. 

Experiment  384.  —  Connect  one  end  of  a  3-pound  coil  of  insulated 
copper  wire,  No.  20,  to  one  of  the  mains  of  a  direct  current,  incan- 
descence lighting  circuit,  and  the  other  end  to  a  short  piece  of  No.  6 
copper  wire.  Connect  another  piece  of  No.  6  copper  wire  to  the  other 
main.  Bring  the  free  ends  of  the  No.  6  wires  into  contact,  and  slowly 
separate  them.  A  flashing  arc  will  follow  the  wires  for  a  short  distance 
and  then  break.  Bring  the  wires  into  contact  again,  separate  them, 
and  try  to  maintain  the  arc.  Notice  that  the  arc  is  tinted  green  by 
the  vapor  of  the  copper.  The  wires  will  become  hot  and  their  ends 
will  be  melted. 

Experiment  385.  —  Tip  one  of  the  terminals  with  a  screw  or  other 
piece  of  steel,  and  connect  the  other-terminal  to  a  block  of  commercial 
zinc.  Set  up  an  arc  between  the  steel  and  the  zinc.  The  pyrotechnic 
effect  is  very  striking.  Replace  the  steel  and  zinc  with  two  pieces  of 
electric  light  carbon.  Notice  that  the  terminals  are  not  melted,  and 
that  the  light  is  a  brilliant  white.  View  the  arc  through  a  piece  of 
smoked  glass,  and  try  to  discover,  from  their  appearance,  which  of 
the  tips  is  the  hotter. 

422.  The  Voltaic  Arc  is  the  most  brilliant  luminous 
effect  of  an  electric  current.  When  carbon  rods  that  form 
part  of  the  circuit  of  a  strong  electric  current  are  sepa- 
rated, as  in  Experiment  385,  their  tips  glow  with  a  brilliancy 
greater  than  that  of  any  other  light  under  human  control. 


548 


SCHOOL  PHYSICS. 


and  the  temperature  of  the  intervening  arc  is  unequalled  by 
that  of  any  other  source  of  artificial  heat. 

(a)  It  is  necessary  to  bring  the  carbons  into  contact  to  start  the 
light.  The  tips  of  the  carbons  become  intensely  heated,  and  the  car- 
bon begins  to  volatilize.  When  the  carbons  are  separated,  the  current 
passes  through  this  intervening  layer  of  vapor  and  the  accompanying 
disintegrated  matter  which  acts  as  a  conductor  of  very  high  resistance. 
The  intense  heat  of  the  voltaic  arc  is  due  to  the  conversion  of  the 
energy  of  the  current  and  not  to  combustion ;  the  arc  may  be  pro- 
duced in  a  vacuum  where  there  could  be  no  combustion. 

(6)  The  constitution  of  the  voltaic  arc  may  be  studied  by  project- 
ing its  image  on  a  screen  with  a  lens. 
Three  parts  will  be  noticed  : 

1.  The   dazzling  white,  concave 
extremity  of  the  positive  carbon. 

2.  The  less  brilliant  and   more 
pointed  tip  of  the  negative  carbon. 

3.  The   globe-shaped   and  beau- 
tifully colored  aureole  surrounding 
the  whole. 

(c)  There  is  a  transfer  of  mat- 
ter across  the  arc  in  the  direction 
of  the  current,  the  positive  carbon 
wasting  away  more  than  twice  as 
rapidly  as  the  negative.  Most  of 
the  light  is  radiated  from  the  cra- 
ter at  the  end  of  the  positive  car- 
bon. 

423.  The  Arc  Lamp  is  es- 
sentially a  device  for  auto- 
matically separating  the  car- 
bons when  the  current  is 
turned  on,  for  "  feeding  "  the  carbons  together  as  they  are 
burned  away  at  their  tips,  and,  in  some  cases,  for  short- 
circuiting  the  lamp  in  case  of  irregularity  or  accident. 


FIG.  439. 


SOME   APPLICATIONS   OF  ELECTRICITY. 


549 


Such  lamps  of  from  one  to  two  thousand  candle-power 
require  an  expenditure,  at  the  dynamo,  of  about  three- 
fifths   of    a   horse-power 
per   lamp.       A    common 
form  of  the  arc  lamp  is 
shown  in  Fig.  440. 


I 


(a)  In  the  arc  lamp  as 
ordinarily  supplied  for  com- 
mercial uses,  the  distance  be- 
tween the  carbon  tips  is  about 
|  of  an  inch.  Such  lamps  re- 
quire a  current  of  from  9  to 
10  amperes,  and  have  a  poten- 
tial difference  between  the 
carbons  of  45  to  50  volts. 
They  are  generally  operated 
in  series,  so  that  the  current 
passes  in  succession  through 
all  the  lamps  on  the  circuit. 
The  resistance  of  the  circuit 
is  thus  increased  by  the  suc- 
cessive addition  of  lamps.  As 
many  as  125  arc  lamps  have 
been  worked  in  series.  The 
E-.M.F.  of  the  current  re- 
quired is  often  3,000,  and 
occasionally  6,000  volts.  Such 
currents  must  be  handled 
with  care,  as  dangerous  results  might  follow  ignorance  or  neglect. 

(6)  The  mechanism  for  separating  and  feeding  the  carbons  consists 
chiefly  of  a  clutch-washer,  w,  a  clutch,  c,  and  a  solenoid  or  "  sucking 
magnet,"  S,  doubly  and  oppositely  wound.  One  of  these  windings 
is  of  coarse  wire  in  series  with  the  carbons ;  the  other  constitutes  a 
high  resistance  shunt  across  the  arc.  The  two  cores  of  the  solenoid 
and  their  connecting  yoke  move  freely  up  and  down,  under  the 
alternating  influence  of  magnetic  attraction  and  gravity.  At  the 
start,  the  carbons  are  in  contact.  When  the  current  is  turned  on, 


FIG.  440. 


550 


SCHOOL  PHYSICS. 


the  series  magnet  lifts  c ;  c  lifts  one  edge  of  to,  thus  causing  it  to 
clutch  and  to  lift  the  rod  that  carries  the  upper  carbon.    The  arc  being 


Fia.  441. 

thus  established,  the  greatly  increased  difference  of  potential  between 
the  arc  terminals  sends  more  current  through  the  oppositely  wound 
shunt  circuit,  thus  weakening  the  lifting  power  of  S.  As  the  carbons 
wear  away  and  the  arc  grows  longer,  the  gradually  increasing  poten- 
tial difference  between  the  terminals  of  the  arc  gradually  forces  more 
current  through  the  shunt  winding  of  the  solenoid,  antagonizing  the 
lifting  effect  of  the  series  magnet  until  gravity  pulls  down  the  cores 
and  the  clutch.  When  w  falls  into  a  horizontal  position,  it  releases 
its  grip  on  the  carbon  rod  and  allows  it  to  slip  down,  thus  reducing 
the  length  of  the  arc,  strengthening  the  current  through  the  series 
coils,  and  reducing  the  current  through  the  shunt  coils.  Ihc 
clutch  is  immediately  lifted  and  the  fall  of  the  carbon  thus  arrested. 
So  delicately  have  these  devices  been  adjusted  that  the  feeding  of  the 


SOME   APPLICATIONS  OF   ELECTRICITY.  551 

carbons  is  as  imperceptible  as  the  movement  of  the  hour  hand  of  a 
watch.  The  current  of  the  shunt  circuit  may  be  made  to  traverse  an 
electromagnet  at  T,  so  that  when  the  arc  becomes  abnormally  long, 
as  it  will  if  the  carbon  does  not  feed  properly,  an  iron  bar  pivoted  at 
i  is  attracted  until  it  closes  a  short  circuit  at  m.  R  represents  a  resist- 
ance properly  adjusted.  In  some  lamps,  the  carbons  are  separated  at 
the  start,  the  shunt  magnet  brings  them  into  contact,  and  the  series 
magnet  separates  them,  thus  establishing  the  arc.  The  shunt  then 
feeds  the  carbons  as  before.  Sometimes  the  "  sucking  magnet "  has 
but  a  single  core.  Many  search  lights  are  made  without  any  auto- 
matic mechanism,  the  carbons  being  fed  by  hand. 

(c)  Since  arc  lamps  are  operated  in  series,  any  particular  lamp 
that  is  to  be  extinguished  must  be  short-circuited.  The  dynamo  is 
provided  with  appliances  for  maintaining  a  uniform  current  strength 
regardless  of  the  number  of  lamps  in  use  on  its  circuit.  When  the 
number  of  lamps  is  increased,  the  voltage  of  the  dynamo  is  corre- 
spondingly increased.  The  connections  of  a  system  of  arc  lights  are 


FIG.  442. 

diagrammatically  shown  in  Fig.  442,  in  which  m  and  n  represent  short- 
circuiting  or  cut-out  switches  ;  C,  the  commutator  of  the  dynamo;  F, 
the  field-magnet  coils  ;  and  R,  a  regulating  resistance.  Any  lamp  may 
be  cut  out  by  closing  a  switch  at  m.  By  closing  the  switch  at  n,  the 
current  is  diverted  from  the  field  magnets.  This  destroys  the  mag- 
netic field  and,  of  course,  destroys  the  current.  When  n  is  open,  the 


552 


SCHOOL  PHYSICS. 


proportion  of  the  current  that  is  sent  through  F  (and,  consequently, 
the  strength  of  the  magnetic  field)  may  be  regulated  by  the  resistance 
that  is  thrown  into  the  shunt  circuit  at  R. 

(d)  Some  arc  lamps  are  made  to  operate  on  incandescence  circuits 
at  constant  potential.  They  are  extinguished  by  open-circuiting 
them.  Incandescence  and  arc  lamps  are  often  operated  from  central 
lighting  stations. 

Experiment  386.  —  Separate  the  terminals  of  a  bichromate  cell  in 
illuminating  gas  escaping  from  an  ordinary  burner.  It  will  be  dim- 
cult  to  make  the  spark  light  the  gas.  Interpose  a  large,  low-resistance 
electromagnet  in  the  circuit,  and  renew  the  attempt.  Explain  the 
increased  magnitude  of  the  spark.  Try  to  light  the  gas  with  a  spark 
from  the  electrophorus ;  from  an  induction  coil;  and  from  a  static 
electric  machine. 

424.  Electric  Gas  Lighting  is  often  effected  by  sparks 
from  the  interrupted  circuit  of  a 
voltaic  battery,  in  which  circuit 
is  a  "  kicking  coil,"  as  illustrated 
in  Experiment  386,  or  by  sparks 
from  the  secondary  of  an  induc- 
tion coil,  or  from  a  machine  for 
the  generation  of  static  electric- 
ity. Burners  like  that  shown  in 
Fig.  443  are  connected  in  series 
in  such  a  circuit. 


FIG.  443. 


425.  Electric  Welding  has  be- 
come a  common  application  of 
the  electric  current.  A  suitable  transformer  changes  an 
alternating  current  of  high  voltage  into  a  current  of 
many  amperes,  the  small  electromotive  force  of  which  is 
adequate  for  the  lo\v  resistance  of  the  metals  to  be  welded. 
It  is  found  that  when  metals  thus  heated  are  welded,  the 


SOME    APPLICATIONS   OF  ELECTRICITY. 


553 


union  is  unusually  firm  and  perfect.  When  a  weld  so 
made  is  finished  off  with  machine-tools,  the  line  of  union 
cannot  be  detected  by  the  eye.  Railway  tracks  are  some- 
times made  continuous  by  this  process. 


Electric  Motors. 

Experiment  387.  —  Fasten  4  iron  strips  to  the  face  of  a  wooden 
cylinder  4  cm.  long  and  6  cm.  in  diameter,  parallel  to  the  axis  of  the 
cylinder,  and  at  equal  distances  from  each  other.  Support  the  axle  so 
that,  as  the  cylinder  turns,  the  iron  strips  will  pass  near  the  end  of  an 
electromagnet,  as  shown  in  Fig. 
444.  When  the  cylinder  is  ro- 
tated, a  square  nut  on  its  axle 
acts  as  a  cam,  forcing  the  vertical 
spring  to  the  right,  and  closing 
an  electric  circuit  at  the  tip  of 
the  set-screw,  s,  four  times  for 
each  revolution.  The  metal  sup- 
port that  carries  s  is  connected 
to  the  binding-post,  b.  The 
metal  support  that  carries  the 
vertical  spring  is  connected  to 
one  terminal  of  the  electromag- 
net, the  other  terminal  of  which 
is  connected  to  the  binding-post,  „  FIG.  444. 

a.  The  nut  is  set  so  that  the  cir- 
cuit is  broken  at  s  just  as  one  of  the  iron  strips  on  the  face  of  the  cylin- 
der comes  to  the  end  of  the  core  of  the  magnet.  The  momentum  of  the 
rotating  cylinder  carries  it  over  the  dead  point  until  the  next  corner 
of  the  nut  forces  the  vertical  spring  into  contact  at  s.  The  apparatus 
will  be  improved  by  placing  a  small  fly-wheel  at  the  other  end  of  the 
axle.  All  of  the  metal  parts,  except  the  core  of  the  magnet,  and 
the  4  strips  011  the  cylinder,  would  better  be  made  of  brass.  Place 
this  apparatus  in  the  circuit  of  several  cells  joined  in  series,  and  set 
the  cylinder  in  rotation  ;  adjust  the  position  of  the  nut  if  necessary 
to  secure  a  continuous  motion. 

Experiment  388.  — Connect   a   small  battery-motor    (one   may  be 
bought  for  a  dollar  or  less)  to  a  number  of  cells  joined  in  series,  and 


554  SCHOOL   PHYSICS. 

interpose  a  low-resistance  galvanoscope  as  indicated  in  Fig.  445.     Hold 

the  shaft  of  the  motor  to  prevent  its  rota- 
tion, and  note  the  reading  of  the  galvano- 
scope. Then  permit  the  motor  shaft  to 
revolve,  and  again  note  the  reading  of  the 
galvanoscope.  The  resistance  of  the  cir- 
cuit seems  to  be  greater  when  the  arma- 
ture is  in  motion  than  when  it  is  at  rest. 

426.    An  Electric  Motor  is  a  de- 
vice for  doing  mechanical  work  at 

the  expense  of  electric  energy.  As  made  for  industrial 
use,  it  is  generally  similar  to  the  dynamo  in  form  and 
construction,  and  is  often  identical  with  it.  The  current 
from  a  dynamo,  perhaps  miles  distant,  is  sent  through  the 
armature  of  the  motor  (the  binding-posts  of  one  machine 
being  connected  to  the  binding-posts  of  the  other),  and 
causes  the  motor  armature  to  revolve  in  a  direction  oppo- 
site to  that  in  which  it  would  revolve  if  the  motor  was 
acting  as  a  dynamo.  This  assumes  that  the  motor  is 
series  wound.  It  thus  appears  that  the  motor  is  based 
upon  the  principle  of  the  reversibility  of  the  dynamo. 
The  pulley  on  the  armature  shaft  is  belted  or  geared  to 
other  machinery. 

(a)  When  the  armature  of  a  dynamo  revolves  in  the  magnetic 
field,  the  motion  develops  a  magnetic  field  for  the  armature  coils  that 
acts  in  opposition  to  that  of  the  field  magnets,  thus  opposing  the 
motion  of  the  armature  and  acting  as  an  addition  to  friction,  etc.,  as 
a  drag  or  counter  torque.  Hence,  the  transformation  of  mechanical 
foot-pounds  into  electrical  watts.  Conversely,  when  a  current  is  sent 
through  the  armature  of  a  dynamo  or  motor  at  rest,  the  opposition 
between  the  magnetic  field  of  the  field  magnets  and  the  magnetic  field 
of  the  armature  coils  produces  a  repulsion  that  causes  the  rotation  of 
the  armature.  Hence  the  transformation  of  watts  into  foot-pounds. 
Any  direct-current  dynamo  will  act  as  an  efficient  motor  when  it  is 


SOME  APPLICATIONS  OF  ELECTRICITY.  555 

supplied  with  a  current  of  the  same  strength  and  potential  as  that 
which  it  yields  when  acting  as  a  dynamo. 

(&)  The  E.M.F.  of  the  inverse  current  generated  in  the  armature 
acts  in  direct  opposition  to  the  E.M.F.  of  the  direct  current.  Repre- 
senting the  E.M.F.  of  the  inverse  current  by  «,  Ohm's  law,  as  applica- 
ble to  this  case,  is  as  follows  :  — 

^  _  E  —  e 
R 

Evidently,  it  is  not  well  to  turn  the  whole  voltage  of  the  actuating 
current  suddenly  upon  a  motor;  the  full  current  might;  do  injury  to 
the  motor  before  its  armature  could  acquire  sufficient  speed  to  produce 
the  inverse  E.M.F.  (e)  that  is  necessary  to  reduce  the  current  to  a  safe 
magnitude. 

(c)  Electric  motors  are  made  in  great  variety  of  form,  and  for 
almost  countless  purposes.  In  our  cities  and  large  villages,  they  are 
placed  on  the  circuits  of  powerful  dynamos  at  central  "power  houses," 
that  correspond  to  electric  lighting  stations,  and  that  are  often  iden- 
tical with  them.  The  convenience,  cleanliness  and  economy  of  the 
electric  motor  have  led  to  its  common  use  for  the  operation  of  light 
machinery,  such  as  fly  and  ventilating  fans,  sewing  machines,  lathes, 
printing  presses,  etc.  On  the  larger  scale,  the  motor  is  used  for  the 
propulsion  of  street  cars,  and  is  even  displacing  the  locomotive  engine 
on  some  railways.  As  a  generator  and  as  a  motor,  the  dynamo  is 
revolutionizing  more  than  one  department  of  the  industrial  world. 

427.  An  Electric  Bell  consists  mainly  of  an  electromag- 
net, E  (Fig.  446),  and  a  vibrating  armature  that  carries  a 
hammer,  H,  that  strikes  a  bell.  One  terminal  of  the  magnet 
coils  is  connected  to  the  binding-post,  and  the  other  ter- 
minal to  the  flexible  support  of  the  armature.  The  arma- 
ture carries  a  spring  that  rests  lightly  against  the  tip  of 
an  adjustable  screw  at  O.  This  screw  is  connected  to  the 
other  binding-post.  The  bell  is  connected  to  a  battery  of 
2  or  3  cells  in  series,  a  key,  a  push-button,  P,  or  some  other 
device  for  closing  the  circuit  being  placed  in  the  line. 

(a)  When  the  circuit  is  closed  by  pushing  the  button  at  P,  the 


556 


SCHOOL  PHYSICS. 


magnet  attracts  the  armature  and  causes  the  hammer  to  strike  the  bell. 

This  movement  of  the  ar- 
mature breaks  the  circuit 
at  C.  E,  being  thus  de- 
magnetized, no  longer  at- 
tracts its  armature,  which 
is  thrown  back  against  the 
end  of  the  screw  by  the 
elasticity  of  the  spring  that 
supports  it.  It  is  then 
again  attracted  and  re- 
leased, thus  vibrating  rap- 
idly and  striking  a  blow 
upon  the  bell  at  H  at  every 
vibration  (see  §  403,  a). 
The  rapidity  of  the  strokes 
depends  largely  upon  the 


FIG.  446. 


length  of  the  pendulum-like  hammer  (see  §  115). 

428.  A  Fire  Alarm  Box  contains  a  crank  which  the 
person  Avho  "  turns  in  "  the  alarm  is  to  pull  down  once. 
This  motion  of  the  crank  winds  up  a  spr-ing  that  drives 
a  train  of  wheel-work  that  puts  in  revolution  a  make-and- 
break  wheel.  The  circumference  of  this  wheel  has  a 
series  of  notches  arranged  to  correspond  to  the  number 
of  the  box ;  e.g.,  if  the  number  of  the  box  is  371,  there 
will  be  three  notches,  separated  by  a  longer  space  from  a 
succession  of  seven  notches,  which  are  followed  at  a  simi- 
lar distance  by  one  notch.  This  notched  wheel  and  an 
arm  that. presses  upon  the  circumference  of  the  wheel 
are  in  the  circuit.  When  the  wheel  revolves,  the  circuit 
is  broken  as  each  notch  passes  under  the  arm.  When  the 
circuit  is  broken,  an  electromagnet  at  the  fire  station  is 
demagnetized.  The  armature  of  the  magnet  is  then  drawn 
back  by  a  spring,  and  strikes  one  blow  upon  a  bell.  A 


SOME   APPLICATIONS  OF  ELECTRICITY.  557 

single  revolution  of  the  inake-aiid-break  wheel  in  the 
distant  alarm  box  gives  a  succession  of  3  strokes,  7 
strokes  and  1  stroke,  thus  indicating  the  number,  371. 
The  wheel- work  may  turn  the  make-and-break  wheel  two 
or  three  times,  thus  repeating  the  alarm  signal.  The 
location  of  Box  371  being  known,  valuable  time  is  saved 
in  determining  the  vicinity  of  the  fire. 

Electrolysis. 

Experiment  389.  —  Put  a  solution  of  sodium  sulphate,  or  any  other 
neutral  salt,  that  has  been  colored  with  an  infusion  of  purple  cabbage 
into  a  V-tube  about  1.5  cm.  in  diameter,  and  supported  in  any  con- 
venient way.     Close  the  ends  of 
the  tube  with  corks  that  carry 
platinum  wires  terminating  in 
narrow  strips  of  platinum  foil 
that  reach  nearly  to  the  bend 
of  the  tube.    Put  this  apparatus 
in  the   circuit   of   2  or  3  cells 
joined  in  series.     In  a  few  min- 
utes, the  liquid  at  the  positive 
electrode   will  be   colored   red, 
and  that  at  the  negative  elec- 
trode, green.     If,  instead  of  col-  JTIG  447. 
oring   the   solution,  a   strip   of 

blue  litmus  paper  is  hung  near  the  positive  electrode  it  will  be  red- 
dened, while  a  strip  of  reddened  litmus  paper  hung  near  the  negative 
electrode  will  be  colored  blue.  These  changes  of  color  are  chemical 
tests ;  the  appearance  of  the  green  or  blue  denotes  the  presence  of  an 
alkali  (caustic  soda  in  this  case),  while  the  appearance  of  the  red 
denotes  the  presence  of  an  acid. 

Experiment  390.  —  Arrange  apparatus  as  shown  in  Fig.  448.     The 
glass  vessel  may  be  made  from  a  glass  funnel,  or  by  cutting  the  bottom 
from  a  wide  mouthed  bottle,  and  may  be  supported  in  any  convenient^ 
way.     The  platinum  electrodes  should  be  about  2  cm.  apart  and  cov- 
ered with  water  (H2O)  to  which  a  little  sulphuric  acid  has  been  added 


558 


SCHOOL  PHYSICS. 


to  increase  its  conductivity.  Fill  two  test-tubes  with  acidulated  water, 
and  invert  them  over  the  electrodes.  When  the  circuit  is  closed, 
bubbles  of  oxygen  escape  from  the  positive  electrode,  and  bubbles  of 
hydrogen  from  the  negative.  The  volume  of  hydrogen  thus  collected 
will  be  about  twice  as  great  as  that  of  the  oxygen.  When  a  sufficient 
quantity  of  the  gases  has  been  collected,  they  may  be  tested;  the 


FIG.  448. 

hydrogen,  by  bringing  a  lighted  match  to  the  mouth  of  the  test-tube, 
whereupon  the  hydrogen  will  burn  ;  the  oxygen,  by  thrusting  a  splinter 
with  a  glowing  spark  into  the  test  tube,  whereupon  the  spark  will 
kindle  into  a  flame.  If  the  gases  thus  separated  are  mixed,  and  an 
electric  spark  produced  in  the  mixture,  the  ions  will  recombine  with 
explosive  violence. 

Experiment  391.  —  Repeat  Experiment  389,  placing  a  solution  of 
copper  sulphate  instead  of  sodium  sulphate  in  the  V-tube.  When  the 
circuit  is  closed,  copper  will  be  deposited  upon  one  of  the  electrodes, 
while  oxygen  will  be  evolved  at  the  other.  Reverse  the  current,  and 
notice  the  disappearance  of  the  copper  from  the  electrode  where  it  was 
first  deposited.  Copper  may  be  dissolved  from  the  platinum  foil  with 
nitric  acid  if  desirable. 

Experiment  392.  —  Melt  some  tin,  and  pour  the  melted  metal  slowly 
into  water.  Dissolve  some  of  this  granulated  tin  in  hot  hydrochloric 
acid,  and  add  a  little  water.  Into  this  hot  solution  of  tin  chloride, 
introduce  electrodes  made  of  tinned  iron  (tin-plate) .  Pass  the  current 


SOME   APPLICATIONS   OF   ELECTRICITY.  559 

of  the  battery  joined  in  series  through  the  liquid,  and  notice  the 
remarkable  tree-like  growth  of  tin  crystals.  Modify  the  experiment 
by  successively  using  solutions  of  lead  acetate,  and  of  silver  nitrate. 

429.  Electrolysis,  etc.  —  The  decomposition  of  a  chemi- 
cal compound,  called  the  electrolyte,  into  its  constituent 
parts,  called  ions,  by  an  electric  current  is  called  electroly- 
sis.    When,  for  example,  water  is  electrolyzed,  the  hydro- 
gen collects  at  the  negative  electrode,  called  the  cathode  ; 
such  an  ion  is  called  a  cation,  and  is  said  to  be  electroposi- 
tive.    The  oxygen  similarly  collects  at  the  positive  elec- 
trode, called  the  anode ;  such  an  ion  is  called   a  anion, 
and  is  said  to  be  electronegative. 

(a)  In  battery  or  in  electrolytic  bath,  the  metallic  or  electroposi- 
tive ion  is  carried  with  the  current  through  the  electrolyte.  Simi- 
larly, when  a  chemical  salt  is  electrolyzed,  the  metallic  base  is  carried 
to  the  cathode,  while  the  acid  constituent  appears  at  the  anode.  The 
amount  of  chemical  decomposition  effected  in  a  given  electrolytic 
bath  in  a  given  time  is  proportional  to  the  current  strength.  This 
principle  has  been  utilized  in  devices  for  the  commercial  measurement 
of  electric  energy. 

Experiment  393.  —  Fasten  a  copper  wire  to  a  silver  coin,  and  a 
similar  wire  to  a  piece  of  sheet  copper  of  about  the  same  size.  Sus- 
pend the  two  pieces  of  metal  in  a  tumbler  containing  a  solution  of 
copper  sulphate.  Connect  the  wire  that  carries  the  silver  to  the 
negative  terminal  of  a  strong  battery  of  cells  joined  in  parallel,  and 
the  other  wire  to  the  other  terminal.  Close  the  circuit,  and  notice 
that  a  firm,  hard  copper  coating  is  deposited  upon  the  silver.  Reverse 
the  current  until  the  copper  is  remoyed  from  the  silver.  Then  con- 
nect the  cells  of  the  battery  in  series,  and  notice  that  copper  is  depos- 
ited upon  the  silver  as  a  spongy  mass  instead  of  a  firm  coating. 

430.  Electrometallurgy  is  the  art  or  process  of  deposit- 
ing certain  metals,  such  as  gold,  silver  and  copper,  from 
solutions  of  their  compounds  by  the  action  of  an  electric 


560  SCHOOL   PHYSICS. 

current.  Its  most  important  applications  are  electroplat- 
ing and  electrotyping.  In  electroplating,  an  adherent 
film  of  metal  is  thus  deposited  on  some  other  material 
(strictly  speaking,  on  metallic  substances  only).  In 
electrotyping,  the  metallic  film  deposited  in  the  bath  is 
not  adherent. 

(a)  For  plating  with  gold,  a  solution  of  the  cyanide  of  gold  is 
generally  used ;  for  plating  with  silver,  a  solution  of  the  cyanide  of 
silver  is  generally  used. 

(b)  The  most  common  forms  of  electrotypes  are  copies  of  medals, 
jewelry,  silverware,  woodcuts,  and  pages  of  composed  type.    The  metal 
most  used  is  copper.     The  form  to  be  copied  is  molded  in  wax ;  the 
face  of  the  mold  is  dusted  with  powdered  plumbago,  in  order  to  make 
it  a  conductor;  the  mold  thus  prepared  is  immersed  in  a  solution  of 
copper  sulphate,  and  subjected  to  the  action  of  a  current  as  illustrated 
in  Experiment  393.     When  the  copper  film  is  thick  enough  (say  as 
thick  as  an  ordinary  visiting  card),  it  is  removed  from  the  mold,  and 
strengthened  by  filling  up  its  back  with  melted  type-metal.      The 
copper  film  and  the  type-metal  are  made  to  adhere  by  means  of  an 
alloy  of  equal  parts  of  tin  and  lead.     The  copper-faced  plate  thus 
produced  is  an  exact  reproduction  of  the  form  from  which  the  mold 
was  made.     When  used  for  printing,  it  is  more  durable  than  the  type 
from  which  it  was  copied. 

(c)  Current  for  electrometallurgical  processes  is  generally  provided 
by  specially  constructed  dynamos  of  low  voltage.     Such  dynamos  are 
called  electroplating  machines,  or  simply  platers. 

Secondary  Cells. 

Experiment  394.  —  Arrange  apparatus  as  in  Experiment  390.  After 
the  passage  of  the  current  for  a  few  minutes,  disconnect  the  battery 
and  put  a  galvanoscope  in  its  place.  The  deflection  of  the  needle 
shows  that  the  "  water  voltameter  "  is  developing  an  electric  current, 
and  illustrating  the  reversibility  of  electrolytic  action. 

Experiment  395.  —  Fit  neatly  to  a  large  tumbler  two  pieces  of  sheet 
lead  as  large  as  can  be  used  without  contact  between  them.  To  each 
lead  plate,  solder  a  copper  wire  about  50  cm.  long.  Fill  the  tumbler 


SOME   APPLICATIONS   OF  ELECTRICITY.  561 

with  dilute  sulphuric  acid.  Connect  the  wires  to  the  terminals  of  a 
high-resistance  galvanoscope,  and  see  if  there  is  any  deflection  of  the 
needle.  Free  one  of  the  lead-cell  wires  from  the  galvanoscope.  Put 
the  lead-cell  and  the  galvanoscope  in  series  in  the  circuit  of  a  battery 
of  several  cells  joined  in  series.  Xote  the  deflections  of  the  galvano- 
scope needle  for  several  minutes.  Quickly  throw  the  battery  out  of 
the  circuit,  and  connect  the  lead-plate  cell  with  the  galvanoscope. 
Note  the  deflection  of  the  needle,  and  the  direction  and  permanency 
of  the  current  now  flowing  from  the^  lead-plate  cell.  Open  and  close 
this  circuit  to  make  sure  that  the  deflection  of  the  needle  is  caused  by 
a  current  from  the  lead  plates,  and  not  by  any  sticking  of  the  instru- 
ment. 

431.  A  Secondary  or  Storage  Battery  is  a  combination 
of  cells  each  of  which  consists  essentially  of  two  plates  of 
metallic  lead  coated  with  red  oxide  of  lead,  and  immersed 
in  dilute  sulphuric  acid.  Sometimes  the  oxide  is  plas- 
tered on  the  roughened  surface  of  the  lead,  and  some- 
times it  is  packed  in  little  pockets  made  in  the  lead  plates 
for  that  purpose.  When  such  a  cell  is  "charged"  by 
passing  an  electric  current  through  it,  the  electrolysis  of 
the  liquid  liberates  oxygen  and  hydrogen.  One  of  these 
ions  peroxidizes  the  coating  of  one  of  the  plates ;  the 
other  ion  reduces,  i.e.,  deoxklizes,  that  of  the  other  plate, 
thus  storing  up  chemical  energy  to  be  given  back  as  an 
electric  current  when  the  poles  of  the  charged  cell  are  con- 
nected, and  the  chemical  action  is  reversed.  Such  a  cell 
or  battery  is  often  called  an  accumulator. 

(a)  In  a  charged  secondary  battery,  the  two  plates  are  unlike,  and 
the  potential  energy  of  chemical  separation  is  converted  into  the 
kinetic  energy  of  an  electric  current,  just  as  with  an  ordinary  or  "  pri- 
mary "  battery.  When  a  secondary  battery  has  run  down,  the  passage 
of  a  current  through  it  will  restore  the  plates  to  their  former  effective 
condition ;  when  a  primary  battery  has  run  down,  a  current  will  not 
thus  restore  the  plates.  Thus,  the  great  advantage  of  the  secondary 
36. 


562  SCHOOL  PHYSICS. 

cell  lies  in  the  fact  that  no  costly  materials  are  consumed,  the  lead 
and  acid  being  as  useful  at  the  end  of  the  operation  as  at  the  begin- 
ning, and  the  coal  consumed  for  the  operation  of  the  dynamo  that 
delivers  the  charging  current  being  much  less  expensive  than  the 
zinc  that  is  consumed  in  the  primary  battery.  Owing  largely  to  the 
mechanical  weakness  of  the  lead  plates,  the  storage  battery  has  not 
yet  proved  the  commercial  success  that  was  expected  a  few  years  ago. 

(6)  The  secondary  cell  has  a  low  internal  resistance,  and  an  E.M.F. 
of  about  2  volts. 

(c)  The  condition  of  the  plates  of  a  charged  secondary  cell  is 
closely  analogous  to  that  of  the  polarized  plates  of  a  primary  cell. 
The  ions  have  a  tendency  to  reunite  by  virtue  of  their  chemical  affin- 
ity, and  thus  to  set  up  an  opposing  E.M.F. ,  as  was  illustrated  in 
Experiment  371.  In  the  electrolysis  of  water,  this  E.M.F.  is  about 
1.45  volts.  Consequently,  an  E.M.F.  of  more  than  1.45  volts  is 
necessary  for  the  decomposition  of  water. 

Telegraph. 

Experiment  396.  —  Connect  two  telephone  receivers,  two  batteries 
and  two  keys  as  shown  in  Fig.  449.  Both  batteries  are  on  open 
circuit.  When  the  key  is  depressed  at  2  or  3,  and  thus  raised  at  1  or 


FIG.  449. 

4,  clicks  will  be  heard  at  T  and  R.  Trace  the  path  of  the  current  in 
each  case.  It  would  be  easy  to  devise  a  code  of  signals  for  communi- 
cation with  such  apparatus  between  two  distant  stations. 

Experiment  397.  —  Support  a  metal  cylinder,  C,  upon  an  axle.  Pivot 
a  metal  bar  at  a  (Fig.  450)  so  that  the  style,  s,  at  its  other  end  may 
rest  upon  the  cylinder.  Connect  battery  wires  to  the  axle  of  the 
cylinder,  and  at  a,  interposing  a  key,  K.  Make  a  paste  by  boiling 
starch  in  water.  Dissolve  about  3  g.  of  potassium  iodide  in  3  or  4 


SOME   APPLICATIONS  OF  ELECTRICITY. 


563 


en.  cm.  of  hot  water,  aud  add  a  little  of  the  paste.  Prepare  a  long 
ribbon  of  white  paper,  and  soak  it  in  the  starch  and  iodide  solution. 
While  the  paper  is  moist,  fasten  one  end  of  it  to  a  spool,  S,  and  turn 
the  handle  so  as  to  draw  the  paper  between  the  style  and  cylinder. 
While  the  paper  is  moving  over  the  surface  of  C,  make  and  break  the 


Fio.  450. 

circuit  at  K  so  as  to  inscribe  a  series  of  blue  dots  and  dashes  on  the 
paper  at  s.  With  A' at  one  station  and  s  at  another,  it  would  be  easy 
for  a  person  at  K  to  send  a  dot  and  dash  message  to  a  person  at  s. 
Consult  the  code  of  signals  given  on  page  564,  and,  with  your  appa- 
ratus, write  the  word  Morse. 

Experiment  398.  —  Arrange  a  line  between  two  stations  as  shown 
in  Fig.  451,  using  galvanoscopes,  G  and  G',  instead  of  the  telephone 
receivers  used  in  Experiment  396.  Each  of  the  keys  consists  of  two 
metal  springs  (e.g.,  1  and  2),  which  are  fastened  to  a  board  at  one  end, 


FIG.  451. 

passing  under  the  metal  strip,  n,  with  which  they  are  in  contact,  and  over 
the  metal  strip,  ro.  When  any  of  these  keys  is  depressed,  it  makes  con- 
tact with  m  or  m',  and  breaks  contact  with  n  or  n'.  When  1  is  de- 
pressed, the  needles  at  G  and  G'  will  be  turned  in  one  direction ;  when 
2  is  depressed,  the  needles  will  be  turned  in  the  other  direction.  Simi- 


564 


SCHOOL  PHYSICS. 


larly,  depressing  3  or  4  will  cause  opposite  deflections  of  the  needles. 
Trace  the  course  of  the  current  for  a  depression  of  each  of  the  four 
keys.  Call  a  deflection  of  the  needle  in  one  direction  a  dot,  and  a 
deflection  in  the  opposite  direction  a  dash,  and  signal  the  word  Kelvin. 

432.  The  Electromagnetic  Telegraph  is  a  device  for  trans- 
mitting intelligible  messages  at  a  distance  by  means  of 
interrupted  electric  currents.  It  consists  essentially  of  a 
line-wire  or  main  conductor  ;  a  battery  or  dynamo  for  the 
generation  of  the  current  ;  a  transmitter  or  key  ;  and  an 
electromagnetic  receiving  instrument.  The  use  of  the  tele- 
graph on  a  commercial  scale  is  chiefly  due  to  S.  F.  B. 
Morse  of  New  York.  The  system  devised  by  him  about 
1844  is  still  in  general  use. 

(a)  The  Morse  code  of  signals  is  as  follows  :  — 


LETTERS,  ETC. 

FIGURES. 

a  

Tc  

u  

\  . 

b  

1  

i'  

'2  

c  -  -    - 

m  

w  

'4  

d  

n  

X  

4  

e  - 

o  -  - 

y.  -       .. 

5  

f 

« 

J  ~ 

P  ~ 

&     ~     -     * 

g  

q  

If  

7  

h  

r  - 

8  

f  -  - 

s  

f  

9  

j  

/  

.  

0  

To  prevent  confusion,  a  small  space  is  left  between  successive  letters, 
a  longer  one  between  words,  and  a  still  longer  one  between  sentences, 
thus :  — 


H    e      w     1      1       1 


m 


a    t 


ten 


(£>)  The  line-wire  is  most  commonly  made  of  iron,  coated  with  zinc 
or  copper.  It  connects  the  apparatus  at  the  several  stations  and  is 
carefully  insulated.  When  the  stations  are  far  distant  from  each 
other,  the  ends  of  the  line-wire  are  connected  to  large  metallic  plates 
buried  in  the  earth  (see  Fig.  457),  or  otherwise  "  grounded."  Whether 


SOME  APPLICATIONS  OF  ELECTRICITY. 


565 


FIG.  452. 


the  earth  is  considered  as  a  conductor,  so  that  the  part  between  the 
grounded  plates  constitutes  the  return  part  of  the  circuit,  or  as  a  great 
"reservoir  of  electricity"  from  which  current  is  drawn  at  one  end  of 
the  line  and  into  which  current  is  discharged  at  the  other,  its  use 
greatly  reduces  the  cost  and  the  resistance  of  the  circuit. 

(c)  The  battery  generally  consists  of  many  gravity  cells  joined  in 
series.  A  dynamo  is  often  used  instead. 

(</)  The  transmitter  or  key  is  a  current  interrupter  manipulated  by 
the  operator.  It  consists  essentially  of  a  metal  lever,  Z,  pivoted  at 
aa,  and  connected  to  the  line  by  the 
screw  at  m  which  is  insulated  from 
the  base,  and  the  screw  at  n  which  is 
connected  to  the  base  and  lever. 
When  the  handle  of  the  lever  is  de- 
pressed, a  platinum  point  on  the  under 
side  of  the  lever  makes  contact  with 
another  platinum  point  at  e,  and  closes 
the  circuit.  The  motion  of  the  lever  is  limited  by  a  set-screw  at  its 
further  end.  When  the  key  is  not  in  use,  the  switch,  s,  is  turned  for 
the  purpose  of  closing  the  circuit  at  that  point. 

(e)  The  Morse  register  is  represented  in  Fig.  453.  The  armature, 
Ay  is  supported  at  the  end  of  a  lever,  and  over  the  cores  of  the  magnet 

bobbins,  M.  A  spring,  S, 
lifts  the  armature  when  the 
cores  are  demagnetized  on  the 
breaking  of  the  circuit  by 
the  operator  at  the  key.  When 
A  is  pulled  down  by  M,  a  style 
or  pencil  at  P  is  pressed  against 
7?,  a  paper  ribbon  that  is  drawn 
along  by  clock  work.  This 
style  may  be  made  to  record 
upon  the  paper  a  dot-and-dash 
communication  sent  by  the 
operator  at  a  key,  perhaps  hundreds  of  miles  away.  Such  registers 
are  little  used  nowadays,  most  operators  reading  by  sound,  i.e.,  de- 
termining the  message  from  the  clicks  of  the  magnet  armature. 

(/)  In  the  Morse  system,  just  described,  a  given  wire  can  trans- 
mit only  one  message  at  a  time.  By  what  is  known  as  the  duplex 
system,  a  wire  may  be  made  to  convey  two  messages,  one  each  way, 


FIG.  453. 


566 


SCHOOL  PHYSICS. 


at  the  same  time,  without  conflict.  By  what  is  known  as  the  quad- 
ruplex  system,  a  wire  may  be  made  to  carry  four  messages,  two  each 
way,  at  the  same  time.  The  multiplex  system  enables  the  sending  of 
six  or  more  messages  in  the  same  direction  at  one  time. 

(g)  Experiment  398  illustrates  the  action  of  a  receiver  often  used 
with  long  submarine  cables.  The  minute  motions  of  the  needle  are 
rendered  visible  by  the  use  of  a  mirror  galvanoscope.  (See  Fig.  391.) 
There  are  several  telegraphic-printing  systems,  the  object  of  which  is 
to  print  the  message  directly  upon  paper  as  it  is  received.  Fac-simile- 
telegraphy  has  also  been  accomplished.  In  the  so-called  rapid  system, 
the  message  is  first  prepared  by  punching  a  series  of  holes  in  a  strip 
of  paper,  each  perforation  or  group  of  perforations  representing  a 
letter.  This  strip  of  paper  is  rapidly  passed  under  metal  points  con- 
nected with  the  line-wire.  At  each  perforation,  a  point  passes  through 
the  paper  and  closes  the  circuit.  At  the  other  end  of  the  line,  a  band 
of  chemically  prepared  paper  is  drawn  rapidly  under  a  style  connected 
with  the  line-wire.  The  current  that  is  interrupted  at  the  sending 
station  makes  a  series  of  stains  on  the  prepared  paper  at  the  receiving 
station,  as  is  illustrated  in  Experiment  397.  As  the  transmission 
and  recording  are  automatic,  the  messages  may  be  sent  in  rapid 
succession. 

Experiment  399.  —  Put  a  key  and  the  apparatus  shown  in  Fig.  392 
in  series  in  the  circuit  of  a  voltaic  cell.  Keeping  the  Morse  alphabet 
in  mind,  try  to  signal  one  of  the  words  similarly  used  in  Experiments 
397  and  398.  Consider  a  short  interval  between  two  clicks  to  be  a 

dot,  and  a  longer  in- 
terval to  be  a  dash. 


433.  The  Sounder 
is  a  telegraphic  re- 
ceiver consisting  of 
an  electromagnet, 
and  a  pivoted  ar- 
mature that  plays 
up  and  down  be- 
tween its  stops  as 
the  circuit  is  alter- 


FIG.  454, 


SOME   APPLICATIONS  OF  ELECTRICITY. 


567 


nately  made  and  broken.  The  message  is  "  read  by  sound, " 
i.e.,  from  the  clicks  made  by  the  armature,  substantially  as 
indicated  in-  Experiment  399.  A  sounder  generally  has  a 
resistance  of  from  3  to  5  ohms. 

Experiment  400.  —  Fasten  a  wire  to  the  apparatus  used  in  Experi- 
ment 399,  so  that  when  the  armature  descends,  the  free  end  of  the 
wire  will  be  dipped  into  mercury  in  the  cup  at  c.  Arrange  the 


FIG.  455. 

apparatus  as  shown  in  Fig.  455,  placing  a  sounder  or  a  telephone 
receiver  at  T.  As  the  key  is  worked  at  K,  the  secondary  or  "  local  " 
circuit  is  made  and  broken  ate,  and  clicks  are  produced  by  the  instru- 
ment at  T. 

434.    The  Relay.  —  With  a  long   main-line  and  many 
instruments      i  n 
circuit,    the     re- 
sistance  may   be 
so    great    as    to 
render  the  main- 
battery      current  _ 
so  feeble  that  it  FlG-  456- 
cannot  operate  the  sounder  with  sufficient  energy  to  render 


568 


SCHOOL  PHYSICS. 


FIG.  457. 


the  signals  distinctly  audible. 
This  difficulty  is  met  by  intro- 
ducing a  "local  battery,"  and 
a  "  relay"  at  each  station  on 
the  line.  The  relay  (Fig.  456) 
is  an  electromagnet  made  of 
many  turns  of  fine  wire  of 
which  the  terminals,  a  and  6, 
are  connected  with  the  main 
line.  This  magnet  operates  an 
armature  lever,  e^  the  end  of 
which  strikes  against  a  metal 
contact-piece  and  thus  closes  the 
local  circuit  through  the  termi- 
nals, c  and  d.  The  resistance 
of  relays  varies  from  50  to  500 
ohms.  The  "Western  Union" 
standard  relay  has  a  resistance 
of  150  ohms. 


(a)  -The  arrangement  of  instru- 
ments is  best  studied  at  a  telegraph 
station,  one  or  more  of  which  may 
be  found  at  almost  any  town  or  rail- 
way station.  The  general  features  of 
the  "  plant "  are  represented  by  the 
diagram  shown  in  Fig.  457.  The  pupil 
will  probably  find  the  key,  sounder  and 
relay  on  a  table,  and  the  local  battery, 
&,  under  the  table.  The  keys  being 
habitually"  closed,  the  current  passes 
through  all  relays  on  the  line,  the 
current  being  continuous  except  when 
a  message  is  being  sent  from  some 
office.  When  an  operator,  in  sending 


MHIVERSITY  OF  CAUFORN,. 

DEPARTMENT  OF  PHVSI<W  * 

SOME  APPLICATIONS  OF  ELECTRICITY.          J    569 


a  message,  opens  his  key,  the  breaking  of  the  circuit  demagnetizes  the 
relays,  and  allows  their  springs  to  draw  back  the  armature  levers,  e. 
This  breaks  each  local  circuit,  and  demagnetizes  each  sounder,  the 
spring  of  which  raises  its  armature.  Things  are  now  as  shown  in  the 
diagram,  which  also  represents  the  condition  of  affairs  at  every  other 
station  on  the  line.  When  a  message  is  sent  from  any  station,  each 
relay  lever,  e,  acts  as  a  key  to  its  local  circuit,  it  and  the  sounder 
armature  working  in  correspondence  with  the  motions  of  the  key  at 
the  sending  station.  Of  course,  the  message  may  be  read  from  any 
sounder  on  the  line. 

(&)  If  the  local  circuit  at  New  York  (see  Fig.  457)  is  lengthened 
so  as  to  reach  thence  to  Boston,  and  the  local  battery,  b,  is  increased 
to  the  size  of  a  main  battery,  B  (ground  connections  being  made,  of 
course),  the  relay  at  Xew  York  will  transmit  to  Boston  the  message 
received  from  Cleveland.  In  such  cases,  the  relay  at  Xew  York 
becomes  a  repeater. 

Experiment  401. —  Put  a  telephone  receiver  in  circuit  with  a  bat- 
tery and  two  electric-light  carbon  pencils 
as  shown  in  Fig.  458.  Vary  the  resist- 
ance of  the  circuit  by  pressing  the  points 
of  the  pencils  together,  and  notice  the 
harsh,  grating  sound  heard  in  the  tele- 
phone. 

435.  The  Microphone  itr  an  in- 
strument for  augmenting  small 
sounds.  Its  action  is  based  011 
the  fact  that  when  substances  of 
low  conductivity  are  placed  in  an 
electric  circuit,  the  resistance  of 
the  circuit  is  diminished  by  even  a  very  small  pressure. 

(a)  In  one  of  the  simplest  forms  of  the  microphone,  a  piece  of  char- 
coal, 6  (Fig.  459),  is  held  between  two  other  pieces  of  carbon,  a  and  c, 
in  such  a  way  as  to  be  affected  by  the  slightest  vibrations  carried  to  it 
by  the  air  or  any  other  medium.  The  external  pieces  being  put  into 


FIG.  458. 


570  SCHOOL  PHYSICS. 

circuit  with  a  battery,  and  a  telephone  receiver  held  at  the  ear,  "  the 

sounds  caused  by  a  fly  walking  on  the 
wooden  support  of  the  microphone  ap- 
pear as  loud  as  the  tramp  of  a  horse." 


Experiment    402.  —  Wind    4  oz.   of 
No.   22   insulated  copper  wire  into   a 
coil,  A,  that  has  an  internal  diameter 
lil'!iil!l!ill|li^  of  1  cm.,  and  connect  its  terminals  to 

FIG  459  ~  those    of    a    telephone    receiver    (Fig. 

379).  Put  a  similar  coil,  J5,  in  the  cir- 
cuit of  a  series  battery  of  three  or  four  voltaic  cells.  Lay  B  on 
a  block  of  iron  (e.g.,  a  stove  cover  or  a  flat-iron),  place  A  upon 
it,  and  insert  a  soft  iron  core  vertically  in  the  openings  of  the  two 
coils.  Place  a  similar  iron  bar  on  end,  close  to  the  coils  and  par- 
allel with  the  iron  core.  Holding  the  telephone  receiver  to  the 
ear,  quickly  lay  a  soft  iron  strip  upon  the  upper  ends  of  the  two 
iron  rods.  A  click  will  be  distinctly  heard  in  the  telephone  receiver. 
Modify  the  experiment  by  replacing  the  second  iron  rod  by  a  piece 
of  gas  pipe  of  the  same  length,  and  with  an  internal  diameter  a  little 
greater  than  the  external  diameter  of  the  coils.  Put  the  iron  core 
and  the  two  coils  that  it  carries  into  the  gas  pipe,  and  stand  the  com- 
bination on  end,  close  the  magnetic  circuit  with  a  soft  iron  strip,  and 
listen  at  the  telephone  as  before. 

436.  The  Telephone  is  an  instrument  for  the  transmission 
of  articulate  speech  to  a  distant  point  by  the  agency  of  elec- 
tric currents.  The  process  consists  essentially  in  the  trans- 
mission of  electric  pulses  that  agree  in  period  and  phase 
with  sound  waves  in  air.  These  pulses,  by  means  of  an 
electromagnet,  cause  a  plate  to  vibrate  in  such  a  way  as  to 
agitate  the  air  in  a  manner  similar  to  the  original  disturb- 
ance, and  thus  to  reproduce  the  sound. 

(a)  The  Bell  telephone  receiver  (see  Fig.  379)  is  a  magneto-electric 
device,  and  is  represented  in  section  by  Fig.  460.  A  is  a  permanent 
bar  magnet  around  one  end  of  which  is  wound  a  coil,  £,  of  carefully 
insulated  fine  copper  wire.  The  terminals  of  B  are  connected  to 


SOME   APPLICATIONS  OF  ELECTRICITY. 


571 


the  binding-posts  at  D.    A  soft,  flexible  sheet-iron  disk  or  diaphragm, 

E,  is  held  by  a  conical 

mouth-piece     or     ear 

trumpet      across     the 

face  of  -B,  near  to  but 

not  quite  touching  the 

end  of  A .     The  outer 

case  is  made  of  wood, 

or  of  hard  rubber. 
(6)  When  a  person 

speaks  into  the  mouth-  FIG.  460. 

piece,  the  sound  waves 

beat  upon  the  diaphragm  and  cause  it  to  vibrate.     The  nature  of  these 

vibrations  depends  upon  the  loudness,  pitch  and  timbre  of  the  sounds 

uttered.  Each  vibration  of  the  dia- 
phragm modifies  the  magnetic  cir- 
cuit of  the  receiver,  varying  the  lines 
of  force  that  pass  through  B,  and 
thus  generating  electric  pulses  in 
the  wire  when  the  circuit  is  closed. 
When  E  approaches  B,  a  current 
flowrs  in  one  direction ;  when  E  moves 
the  other  way,  the  current  flows  in 
the  opposite  direction.  "It  is  as 

if  the  close  approach  and  quick  oscillation  of  the  piece  of  soft  iron 

fretted  or  tantalized  the  magnet,  and  sent  a  series  of  electrical  shud- 
ders through  the  iron  nerve." 

(c)  The  currents  generated  in  a  Bell  telephone  as  just  described 
may  be  sent  through  a  similar  instrument,  at  a  distance  of  several 

LINE  WIRE 


FIG.  461. 


• 


- 


FIG.  462. 


572 


SCHOOL   PHYSICS. 


miles,  perhaps.  The  earth  may  form  part  of  the  circuit,  as  shown  in 
Fig.  462,  but  a  return  wire  or  complete  metallic  circuit  is  preferable. 
When  the  current  generated  at  E  flows  in  such  a  direction  as  to 
reinforce  the  magnet  at  A',  the  latter  attracts  E'  more  strongly  than 
it  did  before.  When  the  current  flows  in  the  opposite  direction,  it 
weakens  the  magnetism  of  A',  which  then  attracts  E'  less.  The  disk, 
therefore,  flies  back.  Thus,  the  vibrations  of  E'  keep  step  with  those 
of  E,  and  produce  sound  waves  that  are  very  faithful  counterparts  of 
those  that  fell  upon  E.  The  sound  thus  produced  at  E'  is  feeble, 
but,  when  the  receiving  instrument  is  held  close  to  the  ear  of  the 
listener,  the  sound  is  clear,  and  the  articulation  remarkably  distinct. 
Conversation  may  be  carried  on  between  moderately  distant  stations 
with  this  apparatus,  no  battery  being  necessary. 

437.  The  Transmitter  is  a  microphone  adapted  for  the 
transmission  of  telephonic  messages  and,  in  general  prac- 
tice, is  so  used,  better  results  being  thus  secured  than  is 
possible  when  the  transmitter  and  receiver  are  identical 
in  form. 

(a)  In  the  Blake  transmitter,  a  diaphragm  is  supported  back  of 
a  mouthpiece,  as  in  the  Bell  telephone.  Back  of  the  center  of  the 
diaphragm  is  the  point  of  a  spring,  m,  that  carries  a  small  platinum 


LINE  WIRE. 


1 


ARTH          EARTH- 


FIG.  463. 

ball  that  makes  gentle  contact  with  the  diaphragm.  Back  of  this 
is  a  spring,  n,  that  is  insulated  from  ra,  and  that  carries  a  carbon 
button,  B,  that  rests  lightly  against  the  platinum  ball.  The  ball,  the 
button,  and  the  primary  of  an  induction  coil  are  put  in  series  in 
the  circuit  of  a  voltaic  battery,  D,  as  shown  in  Fig.  463.  The  varia- 


SOME   APPLICATIONS   OF   ELECTRICITY. 


573 


tions  in  the  resistance  of  this  circuit,  caused  by  the  varying  pressure 
and  surface  contact  between  the  platinum  and  the  carbon,  cause 
variations  in  the  current  that  flows  through  the  primary  of  the  induc- 
tion coil,  and  thus  induce  currents  in  the  secondary  of  the  coil.  One 
of  the  terminals  of  the  secondary  is  connected  through  a  receiving 
instrument,  R,  to  the  earth,  and  the  other  terminal  to  the  line-wire 
leading  to  another  station,  as  diagrammatically  indicated  in  Fig.  463. 
As  previously  suggested,  a  complete  metallic  circuit  is  preferable  to 
the  earth  connections.  The  induced  currents  correspond  closely  to 
the  pulsations  produced  in  the  primary  current  by  the  vibrations 
of  the  diaphragm  of  the  transmitter,  and  in  turn  set  up  vibrations  in 
the  diaphragm  of  the  receiver  at  the  other  station  which,  accordingly, 
sends  off  sound  waves  similar  to  those 
that  disturbed  the  diaphragm  of  the 
transmitter.  An  electric  bell,  shown 
at  E  in  Fig.  464,  is  placed  at  each 
station.  It  is  rung  by  a  small  mag- 
neto at  the  sending  station  for  the 
purpose  of  attracting  the  attention 
of  the  person  at  the  receiving  station. 
When  the  speaker  or  the  listener  lifts 
the  receiver,  B,  from  the  hook  that 
carries  it,  as  shown  in  Fig.  464,  the 
upward  motion  of  the  hook  cuts  the 
magneto  and  the  bells  from  the  circuit, 
and  completes  the  connections  sub- 
stantially as  shown  in  Fig.  463.  - 

(6)  The  long  distance  transmitter, 
represented  at  C  in  Fig.  464,  differs 
from  the  Blake  transmitter  chiefly  in 
the  use  of  a  carbon  that  is  granular 
instead  of  hard,  and  in  the  use  of  two 
or  three  cells  instead  of  one. 

(c)  In  most  cities  and  villages,  the 
telephones  are  connected  by  wires 
with  a  central  station,  called  a  tele- 
phone exchange.  The  exchange  may 
thus  be  connected  with  hundreds  of 
houses  in  all  parts  of  the  city,  or  even 
in  different  cities.  Upon  request  by  FIG.  464. 


574  SCHOOL  PHYSICS. 

telephone,  the  attendant  at  the  central  station  connects  the  lino  from 
any  instrument  with  that  running  to  any  other  instrument.  Long 
distance  telephony  has  been  so  nearly  perfected  that  it  is  common  to 
carry  on  conversation  between  places  as  far  distant  as  Boston  or 
New  York  and  Chicago. 

438.  The  Bolometer  is  an  instrument  designed  for  meas- 
uring very  small  variations   in  the   intensity  of   radiant 
energy  by  the  alteration  of  electrical  resistance  produced 
in  a  metallic  conductor  by  changes  of  temperature. 

(a)  Two  narrow  and  very  thin  strips  of  platinum  or  of  iron  are 
made  two  adjacent  arms  of  a  Wheatstone  bridge,  the  other  two  arms 
being  any  convenient  adjustable  resistance.  A  delicate  galvanometer 
is  placed  in  the  "  bridge."  The  radiation  to  be  measured  is  allowed  to 
fall  upon  one  of  these  strips,  while  the  other  strip  is  shielded  from  it 
by  a  screen.  The  absorption  of  the  radiant  energy  by  the  strip 
increases  the  resistance  of  the  strip,  and  thus  destroys  the  balance 
and  deflects  the  galvanometer  needle.  With  such  an  instrument, 
changes  of  temperature  as  minute  as  a  hundred-thousandth  of  a 
degree  centigrade  have  been  measured,  and  still  smaller  variations 
may  be  detected. 

439.  A  Lightning  Rod  is  a  metallic  conductor  placed 
on  a  building  as  a  protection  from  lightning.     When  an 
electrified  cloud  floats  over  a  building,  the  latter  is  oppo- 
sitely electrified  by  induction.       The  electrification  of  the 
building  escapes  from  the  pointed  conductor,  and  tends  to 
neutralize  the  electrification  of  the  cloud.     Its  action  may 
proceed  too  slowly  to  keep  down  the  rapidly  rising  poten- 
tial of  the  cloud  and  to  prevent  the  disruptive  discharge, 
but  even  then  the  rod  tends  to  protect  the  building  by 
offering  a  path  of  less  resistance.     The  discharge  does  not 
always  follow  the  path  of  least  resistance,  but  the  protec- 
tion is  probable.      The  discovery  of  the  oscillatory  char- 


SOME   APPLICATIONS  OF  ELECTRICITY.  575 

acter  of  the  discharge  has  largely  modified  the  character  of 
the  protection  recommended. 

(a)  In  lightning  protection,  the  following  facts  should  be  kept  in 
mind  :  the  surface  of  the  rod  is  of  more  importance  than  sectional 
area ;  iron  is,  at  least,  as  good  as  copper ;  the  upper  end  should  have 
several  branches  terminating  in  sharp  points  that  are  plated,  or  other- 
wise protected  from  rust  or  corrosion;  very  little  reliance  should  be 
placed  on  the  so-called  "  area  of  protection  " ;  a  rod  towering  high 
above  the  roof  is  not  as  good  as  many  smaller  ones  along  the  ridge  of 
the  roof  ;  the  conductor  should  be  continuous  and  run  to  earth  by  the 
most  direct  path,  avoiding  sharp  bends,  and  going  deep  enough  to  be 
sure  of  a  good  connection  with  a  stratum  that  is  always  moist ;  owing 
to  the  high  potential  involved  and  the  brief  duration  of  the  discharge, 
all  possible  paths  should  be  provided,  and  metallic  surfaces  should  be 
independently  connected  to  earth ;  bury  terminal  earth-plates  in 
damp  earth  or  running  water,  and  do  not  imagine  that  you  can  overdo 
the  matter  of  making  a  good  ground  connection ;  insulators  should 
not  be  used  to  hold  the  rod  in  position.  Next  to  a  poor  "  ground," 
the  chief  defects  likely  to  occur  are  blunted  points,  and  breaks  in  the 
continuity  of  the  rod.  For  ordinary  dwellings  in  city  blocks  (not 
unusually  exposed)  lightning  rods  are  hardly  necessary,  but  scattered 
houses,  especially  those  built  on  hillsides,  should  be  thus  protected. 

(6)  According  to  Professor  Barker,  the  cheapest  way  to  protect  an 
ordinary  house  "is  to  run  common  galvanized-iron  telegraph-wire  up 
all  the  corners,  along  all  the  ridges  and  eaves,  and  over  all  the  chim- 
neys, taking  these  wires  down  to  -the  earth  in  several  places  and,  at 
each  place,  burying  a  load  of  coke  around  the  wire  in  order  to  estab- 
lish at  each  point  an  efficient  connection  with  the  ground." 


CLASSROOM  EXERCISES. 

1.  A  dynamo  is  feeding  16  arc  lamps  that  have  an  average  resistance 
of  4.56  oHms.  The  internal  resistance  of  the  dynamo  is  10.55  ohms. 
What  current  does  the  dynamo  yield  with  an  E.M.F.  of  838.44  volts  ? 

Ans.  10.04  amperes. 

2.  If  a  wire  about  18  inches  long  is  attached  to  one  electrode  of  a 
cell,  and  the  other  electrode  is  momentarily  touched  with  the  other  end 
of  the  wire,  a  minute  spark  may  be  noticed  at  the  instant  of  breaking 
the  circuit.  If  the  wire  is  bent  into  a  scalariform  or  ladder-like  shape 


576  SCHOOL  PHYSICS. 

and  the  experiment  repeated,  the  spark  will  be  greater  than  before. 
If  the  form  of  the  external  circuit  is  again 
changed  by  winding  the  wire  into  a  spiral 
(as  shown  in  Fig.  465),  the  spark  will  be 
still  greater.  Explain  the  increase  in  the 
spark. 

„  3.  A  dynamo  is  run  at  450  revolutions, 

developing  a  current  of  9.925  amperes. 
This  current  deflects  the  needle  of  a  tangent  galvanometer,  60°. 
When  the  speed  of  the  dynamo  is  sufficiently  increased,  the  galvanom- 
eter shows  a  deflection  of  74°.  What  is  the  current  developed  at 
the  higher  speed  ?  Ans.  20  amperes. 

4.  The  current  running  through  the  carbon  filament  of  an  incan- 
descence lamp  was  found  to  be  1  ampere.     The  difference  of  potential 
between  the  two  terminals  of  the  lamp  was  found  to  be  30  volts.    What 
was  the  resistance  of  the  lamp  ? 

5.  The  hot  resistance  of  a  16-c.p.  incandescence  lamp  is  240  ohms. 
The  lamp  is  placed  in  a  110-volt  circuit.      («)  What  current  flows 
through  the  lamp  ?     (ft)  How  many  watts  are  expended  in  the  lamp? 
(c)  What  is  the  consumption  of  energy  per  candle  power? 

Ans.  («)  0.46  ampere;  (&)  50.6  watts;  (c)  3.16  watts. 

6.  I  want  to  place,  in  series,  10  incandescence  lamps,  each  of  25 
ohms  resistance  ;  the  line- wire  is  to  be  200  feet  long  and  its  resistance 
must  be  not  more  than  2  per  cent,  of  the  resistance  of  the  lamps. 
Determine  the  size  of  wire  that  should  be  used.  Ans.  No.  23. 

7.  I  want  to  place  the  same  lamps  abreast.     The  line-wire  is  to  be 
200  feet  long  and  have  a  resistance  of  not  more  than  2  per  cent,  of 
that  of  the  lamps.     Determine  the  size  of  wire  that  should  be  used. 

Ans.  No.  4. 

8.  The  resistance  of  the  normal  arc  of  an  electric  lamp  is  3.8  ohms. 
The  current  strength  is  10  amperes.     What  is  the  difference  of  poten- 
tial between  the  carbon  tips?  Ans.  38  volts. 

9.  The  resistance  of  the  arc  lamp  above  mentioned,  when  the  car- 
bons are  held  together,  is  0.62  ohm.     When  it  is  burning  with  normal 
arc  and  a  10-ampere  current,  what  is  the  difference  of  potential  between 
the  terminals  of  the  lamp  ?  Ans.  44.2  volts. 

10.  A  dynamo  has  an  E.M.F.  of  206  volts,  and  an  internal  resistance 
of  1.6  ohms.     Find  the  current  strength  when  the  external  resistance 
is  25.4  ohms.  Ans.  7.6  amperes. 

11.  A  dynamo  has  an  internal  resistance  of  2.8  ohms.     The  line- 


SOME  APPLICATIONS  OF  ELECTRICITY.  577 

wire  has  a  resistance  of  1.1  ohms  and  joins  the  dynamo  to  3  arc  lamps 
in  series,  each  lamp  having  a  resistance  of  3.12  ohms.  Under  such 
conditions,  the  dynamo  develops  a  current  of  14.8  amperes.  What  is 
the  E.M.F.  ?  Ans.  196.25  voits. 

12.  A  dynamo,  run  at  a  certain  speed,  gives  an  E.M.F.  of  200  volts. 
It  has  an  internal  resistance  of  0.5  of  an  ohm.    In  the  external  circuit 

,are  3  arc  lamps  in  series,  each  -having  a  resistance  of  2.5  ohms.  The 
line  wire  has  a  resistance  of  0.5  of  an  ohm.  I  want  a  current  of  just 
25  amperes.  Must  I  increase  or  lessen  the  speed  of  the  dynamo  ? 

13.  With  an  external  resistance  of  1.14  ohms,  a  dynamo  develops  a 
current  of  81.58  volts  and  29.67  amperes.     What  is  the  internal  resist 
ance  of  the  dynamo  ?  A  ns.  1.61  ohms. 

14.  Upon  trial,  it  was  found  that  a  dynamo  that  was  known  to  have 
an  internal  resistance  of  4.58  ohms  developed  a  current  of  157.5  volts 
and  17.5  amperes.     What  was  the  resistance  of  the  external  circuit  ? 

Ans.  4.42  ohms. 

15.  Three  incandescence  lamps  having  a  resistance  of  39.3  ohms 
each  (when  hot)  were  placed  in  series.     The  total  resistance  of  the 
circuit  outside  of  the  lamps  was  11.2  ohms.     The  current  measured 
1.2  amperes.     What  was  the  E.M.F.?  Ans.  154.92  volts. 

16.  A  dynamo  supplies  current  for  two  incandescence  lamps  in 
series,  each  having  a  hot  resistance  of  97  ohms.     The  other  resistances 
of  the  circuit  amounted  to  12  ohms.     The  current  in  the  first  lamp  was 
1  ampere.     What  was  the  current  carried  by  the  carbon  filament  of 
the  second  lamp  ?     What  was  the  E.M.F.  ? 

17.  A  dynamo  is  required  to  f  urnish  a  9.6-ampere  current  for  60  arc 
lamps.     Assuming  that  a  copper  wire  1  square  inch  in  cross-section 
will  safely  carry  2,000  amperes,  determine  the  proper  size  of  wire  for 
the  Gramme  ring  armature  of  the  dynamo.     In  such  an  armature,  each 
wire  carries  half  the  current.  Ans.  No.  15. 

18.  W7hat  E.M.F.  must  be  generated  by  the  dynamo  mentioned  in 
Exercise  17  if  the  resistance  of  the  line-wire  is  5  ohms,  the  internal 
resistance  of  the  machine  is  16  ohms,  and  the  difference  of  potential 
between  the  terminals  of  each  lamp  is  45  ohms  ? 

19.  Assume  that  the  E.M.F.  of  a  bipolar  dynamo  may  be  deter- 
mined by  the  formula, 

F-.         nks 

"  100,000,000 ' 

In  which  E  represents  the  E.M.F.;  n  the  number  of  lines  of  force 
passing  effectively  through  the  armature ;  k  the  number  of  conductors 
37 


578 


SCHOOL   PHYSICS. 


in  series  on  the  armature ;  and  s  the  number  of  revolutions  that  the 
armature  makes  per  second.  Determine  the  E.M.F.  of  a  dynamo  the 
armature  of  which  makes  780  revolutions  per  minute,  has  120  conduc- 
tors in  series,  and  is  threaded  by  7,200,000  lines  of  force. 

Ans.  112.32  volts. 

20.  What  effect  would  a  slowing  of  the  speed  of  a  dynamo  have 
upon  its  E.M.F.  ? 

21.  Suppose  that  the  armatures  of  two  dynamos  rotate  at  the  same 
speed  in  fields  of  like  intensity.     The  armatures  differ  only  in  that  one 
has  twice  as  many  bobbins  in  series  as  the  other.      How  will  the 
dynamos  compare  in  E.M.F.? 

22.  Suppose  that  the  armature  of  a  dynamo  is  wound  with  No.  8 
copper  wire,  that  it  revolves  at  a  uniform  speed,  and  that  the  potential 
difference  at  the  terminals  of  the  dynamo  is  constant.      What  is  to 
prevent  our  drawing   from   the   machine  a  current   that  is  almost 
unlimited  as  to  strength? 

23.  Suppose  an  adjustable  resistance,  jR,  to  be  cut  into  the  magiietiz- 

4.       _  ing  circuit  of  a  shunt-wound 

dynamo  as  shown  in  Fig. 
466.  How  would  an  in- 
creased resistance  affect  the 
number  of  lines  of  force  that 
pass  through  the  armature, 
A  ?  Could  the  E.M.F.  of  the 
dynamo  be  thus  controlled? 
24.  A  certain  dynamo 
yields  a  current  of  9.6  am- 
peres at  almost  any  voltage 
desired.  I  want  to  send  a 
2-ampere  current  through 
a  coil  that  has  a  resistance 
of  2  ohms.  What  resistance  must  be  put  in  parallel  with  the  coil 
between  the  terminals  of  the  dynamo?  Ans.  0.526  -f  ohms. 

25.  A  system  of  127  incandescence  lamps,  each  fed  at  a  potential 
difference  of  110  volts,  and  with  a  current  of  0.5  of  an  ampere,  is  620 
feet  from  the  dynamo.  Allowing  for  an  absorption  of  four  per  cent, 
of  the  energy  of  the  current  by  the  line-wire,  (a)  what  must  be  the 
voltage  of  the  dynamo?  The  difference  between  the  voltage  of 
the  dynamo  and  that  of  the  lamps  is  the  fall  of  potential  due  to  the 
resistance  of  the  wire.  Applying  Ohm's  law,  divide  this  fall  of  poten- 


FIG.  466. 


ELECTROMAGNETIC   CHARACTER    OF   RADIATION.       579 

tial  by  the  current  required,  and  thus  (ft)  determine  the  total  resist- 
ance of  the  line-wire,  (c)  Determine  the  resistance  of  the  line-wire 
per  foot.  (Y/)  Consult  the  table  in  the  appendix,  and  ascertain  the 
proper  size  of  the  line-wire.  Ans.  (a)  114.58  +  volts. 

26.  The  field  magnet  of  a  shunt-wound  dynamo  is  to  be  made  of 
Xo.  14  copper  wire.     Such  a  wire  cannot  carry  a  current  of  more  than 
15  amperes  without  danger  of  becoming  so  hot  as  to  injure  its  insula- 
tion.     Assume  that  the  dynamo  delivers  current  at  110  volts,  and 
determine  the  length  of  wire  that  must  be  used  in  the  field  magnets 
to  keep  them  from  over-heating. 

27.  Fire  insurance  rules  allow  Xo.  0000  ("  four-naught")  copper 
wire  to  carry  a  current  of  175  amperes,  which  is  sufficient  for  350 
lamps  at  110  volts.     Suppose  that  one  hundred  such  lamps  are  to  be 
placed  a  mile  from  a  central  station,  («)  What  will  be  the  resistance 
of  the  line  if  it  is  made  of  the  wire  above  mentioned?     (ft)  What 
must  the  voltage  at  the  station  be  ? 

Ans.   (a)  0.53856  ohms;  (ft)  136.928  volts. 

28.  I  have  two  telegraph  sounders.     One  of  them  is  made  with  a 
few  turns  of  coarse  wire  ;  the  other  of  many  turns  of  fine  wire.     Try- 
ing them  on  a  long  line  of  great  resistance,  I  find  that  one  works 
satisfactorily  while  the  other  will  not  work  at  all.     Which  sounder 
works  ?     Explain  the  difference  in  the  results  secured  with  the  two 
instruments. 

29.  A  telegraph  line  is  to  be  operated  between  Boston  and  Chicago. 
The  high  resistance  of  so  long  a  line  requires  a  current  of  such  high 
potential  that  there  is  great  difficulty  in  maintaining  the  insulation. 
How  may  this  difficulty  be  removed  ? 

30.  I  find  that  I  can  hear  readily  through  a  telephone  receiver  that 
is  in  circuit  with  several  miles  of  uncoiled  wire,  but  that  when  the 
wire  is  wound  upon  an  iron  core,  thus  making  an  electromagnet,  I 
cannot  hear  through  the  telephone  at  all.     Explain. 


V.    ELECTROMAGNETIC   CHARACTER   OF 
RADIATION. 

V 

440.  Electromagnetic  Rotation,  etc. — When  a  beam  of 
polarized  light  is  passed  through  a  magnetic  field,  the 
plane  of  polarization  is  rotated  in  the  direction  in  which 


580  SCHOOL   PHYSICS. 

an  electric  current  would  have  to  circulate  around  the 
beam  to  produce  the  existing  magnetism.  If  the  beam  is 
reflected  back  so  as  to  traverse  the  magnetic  field  twice  in 
opposite  directions,  the  magnetic  rotation  is  doubled. 
When  a  beam  of  polarized  light  is  reflected  from  the 
polished  pole  of  an  electromagnet,  the  plane  of  polariza- 
tion is  rotated  in  a  direction  contrary  to  that  of  the  mag- 
netizing current.  A  dielectric  under  electrostatic  stress 
becomes  doubly  refracting.  These  and  other  facts  sug- 
gest that  there  is  some  definite  relation  between  elec- 
tricity and  light. 

441.  Electrical  Oscillations.  —  If  an  elastic  cord  is 
stretched  between  two  supports  and  its  middle  pulled  to 
one  side,  it  may  be  allowed  to  return  to  its  normal  posi- 
tion so  gently  as  to  cause  no  vibrations  in  the  cord,  or  it 
may  be  released  so  as  to  set  up  vibrations,  the  frequency 
of  which  will  depend  largely  upon  the  tension  of  the  cord. 
Similarly,  when  a  Leyden  jar  is  discharged  through  a  dry 
linen  thread,  there  is  a  gentle  floAV  of  electrification  from 
one  coat  to  the  other,  and  equilibrium  is  quietly  restored. 
On  the  other  hand,  when  the  charged  jar  is  discharged 
through  a  short  metal  conductor,  the  charge  rushes  sud- 
denly from  one  coat  to 
the  other,  overdoes  its 
work,  and  surges  back 
ONC5  and  forth  with  gradu- 

100,000  . 

ally  weakening  energy 
until  the  two  coats  are 
FlG- 467-  at  the  same  potential. 

(a)  Fig.  467  is  a  graphic  representation  of  such  electrical  oscilla- 
tion, the  heights  of  the  waves  being  proportional  to  the  magnitudes  of 


ELECTROMAGNETIC   CHARACTER  OF  RADIATION.      581 

the  flow,  and  the  lengths  being  proportional  to  the  times  required  for 
the  successive  oscillations.  Fig.  468  shows  a  similar  curve  for  an 
ordinary  alternating  current.  Comparing  the  time  axes  (abscissae)  of 
the  two  curves,  it  is  seen  that  the  curve  of  the  Leyden  jar  may  be 
completed  in  0.00001  of  a  second,  while  the  alternate  current  requires 
0.004  of  a  second  for  a  single  pulse.  Further  comparison  of  the 
curves  shows  a  marked  difference  in  the  rate  of  change,  the  time  inter- 


t -1  SECONDS 


Fia.468. 

val  required,  in  the  first  case,  for  a  drop  from  a  maximum  value  in 
one  direction  to  a  maximum  in  the  other  direction  being  almost 
infinitesimal.  It  also  appears  that  the  alternating  current  curve  is 
strictly  periodic  and  repeats  itself,  while  the  Leyden  jar  oscillations 
gradually  die  away.  It  has  been  shown  that  when  the  resistance  of 
the  circuit  is  negligible,  the  number  and  periods  of  these  oscillations 
per  second  may  be  represented  thus  :  — 

,  or  t  =  2  IT 


In  this  formula,  n  represents  the  frequency,  and  t  the  period  of  oscilla- 
tion ;  K,  the  capacity  ;  and  L,  the  coefficient  of  self-induction.  An 
increase  in  the  values  of  K  and  L  diminishes  the  value  of  n.  By  dis- 
charging a  large  condenser  through  a  high  inductive  resistance,  the 
frequency  of  the  electrical  oscillations  has  been  reduced  to  400  per 
second,  under  which  conditions  the  electric  spark  emitted  a  musical 
tone. 

442.    Electromagnetic  Waves.  —  With  currents  of  slowly 
varying  strength,  magnetic  lines  of  force  surround  the 


582  SCHOOL  PHYSICS. 

conductors  that  carry  the  currents.  When  the  direction 
of  the  current  is  changed,  the  direction  of  the  lines  of 
force  is  changed.  These  lines  of  force  spread  out  from  a 
wire  carrying  an  increasing  current  much  like  the  ripples 
on  a  pond  moving  outward  from  the  center  of  disturbance. 
As  the  current  dies  away,  these  magnetic  lines  of  force 
are  called  in  again.  As  the  current  reverses  its  direction, 
other  lines  of  force  opposite  in  direction  from  the  former 
ones  are  sent  out.  This  alternating  action  sets  up  a  series 
of  waves  that  travels  outward.  So,  when  the  rapidly 
oscillating  motions  of  the  Ley  den  jar  discharge  are  applied 
to  a  conductor,  the  magnetic  ripples  that  are  propagated 
never  return  to  the  conductor  that  generates  them,  but 
continue  on  through  space  like  the  waves  of  radiant  energy. 
Just  as  a  vibrating  tuning-fork  expends  its  energy  in 
producing  air  waves,  so  a  discharging  condenser  sets  up 
vibrations  in  the  medium  of  electrical  action,  whatever 
that  medium  may  be. 

(a)  In  recent  years,  Hertz  and  Nikola  Tesla  have  experimented 
with  these  electromagnetic  waves,  and  have  shown  that  they  may  be 
reflected,  refracted,  and  polarized,  and  that  they  possess  all  the  trans- 
mittive  properties  of  radiant  energy.  They  have  also  shown  that 
their  velocity  is  identical  with  that  of  light,  and  that  indices  of  refrac- 
tion are  the  same  for  electromagnetic  waves  as  they  are  for  the  shorter 
waves  that  are  familiarly  recognized  as  radiant  energy. 

Experiment  403.  —  Provide  two  Leyden  jars  that  are  alike.  Paste 
a  strip  of  tin-foil  so  that  it  touches  the  inner  coat  of  one  of  the  jars, 
passes  over  the  edge,  and  nearly  touches  the  outer  coat  as  shown  at 
a  in  Fig.  469.  From  the  knob  and  the  outer  coat  of  this  jar,  /,  lead 
two  wires.  Tie  these  wires  with  silk  thread  to  the  edges  of  a  plate 
of  glass  that  is  6  or  7  cm.  wide  and  supported  in  a  vertical  plane. 
Connect  a  wire  to  the  outer  coat  of  the  other  jar,  L,  bend  the  wire 
into  a  loop,  and  provide  a  terminal  ball,  B,  as  shown  in  the  figure. 
Bend  the  wire  so  that  B  is  brought  very  near  to  the  knob,  A,  without 


ELECTROMAGNETIC   CHARACTER   OF  RADIATION.      583 

quite  touching  it.  Place  L  near  /,  with  its  wire  loop  in  a  plane  that 
is  parallel  to  that  of  the  suspended  glass  plate.  Charge  L  by  an 
induction  coil  or  an  electrical  machine  so  that  a  stream  of  sparks  snaps 
across  AB.  Connect  the  two  wires  carried  by  /,  by  a  spring  clip,  C. 


FIG.  4fi9. 

Move  the  clip  back  and  forth  along  the  wires  until  you  find  for  it  a 
position  such  that  as  sparks  pass  between  A  and  B,  other  sparks  will 
snap  across  the  gap  at  a.  The  _two  jars  will  then  be  in  "  electrical 
resonance." 

443.  Electrical  Resonance.  —  When  certain  relations  of 
capacity  and  reactance  exist  between  two  electric  circuits, 
electrical  vibrations  of  high  frequency  in  one  of  the  cir- 
cuits will  set  up  electrical  vibrations  in  the  other  circuit. 
The  best  results  are  obtained  when  the  receiving  circuit  is 
so  adjusted  that  its  oscillations  are  synchronous  with  those 
of  the  generating  circuit.  A  receiving  circuit  so  adjusted 
is  called  an  electrical  resonator.  Electrical  resonance  is 
analogous  to  acoustic  resonance,  and  has  been  of  great 


584  SCHOOL  PHYSICS. 

value  in  recent  researches  on  the  electromagnetic  theory 
of  light.  The  adjustment  of  capacity  and  self-induction 
so  as  to  harmonize  the  vibration-frequency  of  the  two  cir- 
cuits, i.e.,  to  establish  resonance,  is  often  a  matter  of  great 
delicacy  and  difficulty.  In  very  exact  adjustments,  minute 
changes  completely  destroy  the  balance,  just  as  they  do  in 
acoustic  resonance. 

444.  The  Hertz  Experiments.  —  In  his  study  of  electric 
waves,  Hertz,  the  first  successful  investigator  in  this  field, 
used  an  "  oscillator "  that  consisted  of  an  induction  coil, 
the  terminals  of  which  carried  two  metal  rods,  t  and  t1, 
that  ended  in  small  metal  balls,  and  that  were  provided 

with  large  movable 
t  t '  1Y  |  R  metal  plates  or 

spheres,     A    and    B. 

The    capacity,   K,    of 

the  system  was  deter- 
FIG-470'  mined  from  the  size 

of  the  plates  or  the  spheres,  A  and  B,  and  the  coefficient 
of  self-induction,  L,  from  the  dimensions  of  the  rods, 
t  and  t1.  Within  certain  limits,  the  value  of  L  could 
be  adjusted  by  varying  the  position  of  A  and  B  upon 
the  rods.  The  values  of  K  and  L  being  known,  the  pe- 
riod of  a  complete  oscillation  could  be  determined  (see 
§  441,  a).  To  reduce  the  wave-length  to  convenient  val- 
ues (say  a  meter  or  two),  the  oscillations  were  made 
rapid;  i.e.,  K  and  L  were  made  small. 

(a)  The  action  of  this  apparatus  generates  two  sets  of  waves  of  the 
same  period ;  one  set  being  electrostatic,  and  the  other,  electromag- 
netic. The  effects  produced  by  these  two  sets  of  waves  may  be 
separately  studied.  The  electrostatic  lines  of  force  extend  between  A 


ELECTROMAGNETIC   CHARACTER   OF   RADIATION.       585 

and  B.  The  electromagnetic  lines  of  force  are  concentric  about  the 
rods,  t  and  i! '.  Hertz's  resonator  was  an  open 
wire  ring  terminally  provided  with  small 
balls,  micrometrically  adjustable  so  that  the 
distance  between  them  could  be  accurately 
measured.  When  this  simple  resonator  is 
made  to  enclose  the  electromagnetic  lines  of 
force  set  up  by  the  oscillator,  induction  sparks 
pass  between  the  terminals  m  and  n.  Adjust- 
ment for  synchronous  effect,  and  placing  the 
resonator  so  that  its  plane  passes  through  the 
axis  of  the  oscillator,  raise  the  sparks  to  their  FIG.  471. 

maximum  value. 

(6)  Anywhere  in  the  field,  sparks  may  be  obtained  between  any  two 
metallic  objects.  Hertz  placed  two  rods  in  the  same  line  and  with 
their  ends  near  together,  and  used  them  as  a  receiver.  He  attached 
sheets  of  tin-foil  to  the  rods,  and  thus  increased  their  capacity,  so  that 
sparks  were  obtained  at  a  distance  of  20  or  30  m.  from  the  oscillator. 
He  found  that  non-conductors  are  transparent  to  the  electric  radia- 
tions, and  that  conductors  act  as  reflectors.  With  waves  reflected  from 
a  zinc-covered  wall,  and  by  moving  the  resonator  about,  he  found 
points  of  maximum  and  minimum  disturbance  corresponding  to  the 
loops  and  nodes  of  a  vibrating  string.  The  wave-lengths  thus  deter- 
mined, multiplied  by  the  frequency  of  vibration  as  calculated  from  K 
and  L,  the  constants  of  the  oscillator,  gave  a  velocity  for  electric  wave 
propagation  that  is  practically  the  same  as  the  velocity  of  light.  He 
also  demonstrated  the  rectilinear_.propagation  of  the  waves,  and  focused 
them  with  a  metallic  parabolic  mirror.  He  refracted  them  with  a 
prism  of  pitch,  and  established  the  index  of  refraction  for  radiations 
of  certain  wave-lengths. 

(c)  Using  more  delicate  apparatus,  Lodge  has  detected  electro- 
magnetic waves  that  had  passed  through  floors  and  walls,  and  at  a 
distance  of  hundreds  of  feet. 


445.  The  Tesla  Experiments.  —  By  means  of  his  oscil- 
lator (§  398),  in  which  the  armature  coils  are  shot,  very 
rapidly  and  shuttle-fashion,  in  and  out  of  the  magnetic 
field,  Nikola  Tesla  has  generated  alternating  currents  of 


586  SCHOOL  PHYSICS. 

higher  frequency,  potential,  and  regularity  than  any  pre- 
viously employed,  and  has  greatly  augmented  the  Hertzan 
effects  and  added  to  them. 

(a)  He  has  shown  that  such  currents  flow  mostly  on  the  outer  sur- 
face of  the  conductor,  as  though  ether  vortices  were  rolled  along  the 
wire  as  a  rubber  band  may  be  rolled  along  a 
pencil,  and  that  the  impedance  of  a  stout  copper 
rod  may  be  hundreds  of  times  as  great  as  that  of 
an  incandescent  lamp  filament,  although  the  ratio 
of  their  resistances  is  the  reverse.  For  instance, 
he  short-circuited  a  lamp  by  a  copper  rod  as  shown 
in  Fig.  472.  Any  ordinary  current,  direct  or 
alternating,  would  melt  the  rod  before  the  lamp 
began  to  glow,  but  Tesla's  current  brilliantly  il- 
luminated the  lamp  and  left  the  rod  cool.  In  fact, 
with  Teslaic  currents,  the  resistance  of  the  lamp 
FIG  472  filaments  counts  for  little  or  nothing,  and  the  fila- 

ment may  as  well  be  short  and  thick  as  long  and 
thin.  More  than  even  this,  the  filament  and  conducting  wires 
may  be  wholly  omitted.  Vacuum  tubes  of  ordinary  glass  held  in 
the  hand  near  the  terminal  of  a  high  frequency  coil  became 
luminous,  as  shown  in  Fig.  473,  clearly  showing  that,  as  the  current- 
frequency  rises,  electrodynamic  conditions  are  left  for  those  that 
are  electrostatic,  and  that  space  itself  "is  all  circuit  if  we  prop- 
erly direct  the  right  kind  of  impulses  through  it."  Tesla  led  a 
small  cable  around  the  walls  of  a  room  40  x  80  feet  in  size,  and  con- 
nected its  ends  to  the  terminals  of  an  oscillator.  In  the  middle  of  the 
room,  he  placed  a  coil-wound  resonator  three  or  four  feet  high  and 
provided  with  two  adjustable  condenser  plates.  These  plates  stood  on 
edge  above  the  end  of  the  coil  and  facing  each  other,  much  as  if  they 
wTere  cymbals  resting  upon  the  head  of  a  bass  drum.  By  adjusting 
the  condenser  plates,  the  resonator  was  so  attuned  that  the  periodicity 
of  the  induced  current  kept  step  with  that  of  the  cable  current.  When 
current  from  the  oscillator  was  sent  along  the  cable  around  the  room, 
powerful  sparks  poured  in  dense  streams  across  the  space  between  the 
cymbal-like  plates  of  the  attuned  condenser  in  the  middle  of  the  room. 
A  potential  difference  of  200,000  or  300,000  volts  is  easily  developed 
in  this  way,  and  the  high-tension  currents  pass  through  the  human 
body  without  injury.  With  a  similar  resonator  similarly  placed  and 


ELECTROMAGNETIC   CHARACTER   OF   RADIATION.      587 

properly  attuned,  an  ordinary  16-c.p.  lamp  was  well  illuminated. 
When  an  110-volt  lamp  was  attached  by  one  terminal  to  a  wire  circle, 
and  the  circle  held  above  the  resonator  coil,  the  lamp  immediately 
lighted  up.  Such  an  illumination  of  such  a  lamp  calls  for  the  expen- 
diture of  more  than  a  tenth  of  a  horse-power,  so  that  at  least  that 


FIG.  473. 

amount  of  energy  was  transmitted  through  free  space,  i.  e.,  without  any 
wire.  By  connecting  to  earth  one  terminal  of  a  coil  in  which  rapidly 
vibrating  currents  are  thus  produced,  and  leaving  the  other  terminal 
free  in  space,  Tesla  produces  striking  effects,  purple  fiery  streams  and 
lightning  discharges  pouring  into  the  air  from  the  tip  of  the  wire  "with 
the  roar  of  a  gas  well." 

Mr.  Tesla  has  secured  his  results  chiefly  because  he  has  "learned  the 
knack  of  loading  electrically  on  the  good-natured  ether  a  little  of  the 
protean  energy  of  which  no  amount  has  yet  sufficed  to  break  it  down 
or  put  it  out  of  temper."  His  experiments  point  toward  the  possibility 
of  telephony  without  any  wire,  i.e.,  by  induction  through  the  air  and, 
in  fact,  some  such  transmission  of  intelligence  has  been  seriously  pro- 
pounded, not  as  a  mere  theoretical  possibility  but  as  a  problem  in 
practical  electrical  engineering. 


588  SCHOOL  PHYSICS. 

446.  The  Electromagnetic  Theory  of  Light.  —  Optical 
and  electrical  phenomena  seem  to  call  for  media  that  have 
identical  properties;  i.e.,  they  indicate  that  the  medium 
of  the  one  is  identical  with  the  medium  of  the  other.  The 
experimental  proof  that  3  x  1010  centimeters  represent 
alike  the  velocity  of  light  and  the  velocity  of  electric 
waves,  indicates  that  the  ether  is  the  common  medium. 
This,  taken  in  connection  with  the  close  relation  estab- 
lished between  specific  inductive  capacity  and  index  of 
refraction,  and  that  between  electric  conductivity  and 
optical  opacity,  and  the  experiments  of  Hertz  and  of  Tesla, 
"  appear  to  prove  beyond  a  question  that  light  is  itself  an 
electrical  phenomenon  and  that  optics  is  a  department  of 
electrics.  To  produce  radiation,  it  is  only  necessary  to 
produce  electric  oscillations  of  sufficiently  short  period." 
This  theory  of  light  as  an  electromagnetic  disturbance  was 
propounded  in  1865  by  Maxwell ;  if  recent  investigations 
do  not  wholly  establish  it,  they  certainly  give  it  very 
strong  support. 

(a)  It  has  been  calculated  that  a  condenser  of  one  microfarad 
capacity  might  generate  electric  waves  1,900  Km.  long ;  a  pint  Leyden 
jar,  waves  15  or  20  m.  long;  and  a  tiny  thimble-like  jar,  waves  1  m. 
long.  Continuing  this  process  to  ascertain  the  size  of  a  circuit  that 
will  give  wave-lengths  comparable  to  those  of  light,  physicists  come 
to  the  suggestion  that  the  ether  waves  that  affect  the  retina  of  the 
human  eye  may  be  produced  by  the  electric  oscillations  of  circuits  of 
atomic  dimensions.  An  atom  of  sodium  vibrates  five  hundred 
million  times  in  one  millionth  of  a  second.  If  we  could  produce 
electric  oscillations  and  maintain  them  at  this  rate,  we  could  produce 
light. 

(fc)  Light  is  ordinarily  produced  by  combustion,  less  than  one  per 
cent  of  the  emitted  energy  being  visible.  "The  problem  of  the  age 
is  to  convert  some  other  form  of  energy  entirely  into  the  energy  of 
light.  That  this  is  possible  in  theory,  Rayleigh  long  ago  showed. 


ELECTROMAGNETIC   CHARACTER  OF   RADIATION.      589 

That  it  is  actually  accomplished  in  Nature,  Langley's  remarkable 
measurements  upon  the  glowworm  abundantly  confirm.  Now  that 
the  mechanism  of  the  process  is  before  us,  it  would  seem  not  impos- 
sible eventually  to  create  and  to  maintain  electric  oscillations  of  the 
frequency  required  for .  light  alone.  When  this  is  done,  the  problem 
of  the  economical  production  of  artificial  light  will  have  been  solved." 

447.  Yesterday,  To-day,  To-morrow.  —  In  the  light  of 
what  has  lately  been  accomplished  by  the  blending  of 
theory  and  practice,  and  of  the  promise  that  comes  from 
the  state  of  unrest  in  which  electrical  science  now  exists, 
it  seems  a  fitting  final  word  to  suggest  that  constant 
study  is  the  price  of  a  clear  understanding  of  conditions 
that  prevail  in  the  domain  of  electricity.  "  Its  theoretical 
problems  assume  novel  phases  daily.  Its  old  appliances 
ceaselessly  give  way  to  successors.  Its  methods  of  pro- 
duction, distribution,  and  utilization  vary  from  year  to 
year.  Its  influence  on  the  times  is  ever  deeper,  yet  one 
can  never  be  quite  sure  into  what  part  of  the  social  or 
industrial  system  it  is  next  to  thrust  a  revolutionary  force. 
Its  fanciful  dreams  of  yesterday  are  the  magnificent 
triumphs  of  to-morrow,  and  its  advance  toward  domination 
in  the  twentieth  century  is  as  irresistible  as  that  of  steam 
in  the  nineteenth." 


APPENDIX. 


1.    Mensurative,  etc. 

TT  =  3.14159. 

Circumference  of  a  circle  =  irD. 

Area  of  a  circle  =  TrR'2. 

Surface  of  a  sphere  =  4irR2  =  7rZ>2. 

Volume  of  a  sphere  =  |7r/t3  =  \irLP. 

Meters  x  3.2809  =  feet. 

Feet  x  0.3048  ^  meters. 

Inches  x  2.54  =  centimeters. 

Cubic  inches  x  16.386  =  cubic  centimeters. 

Cubic  centimeters  x  0.06103  =  cubic  inches. 

Kilogrammeters  x  7.2331  =  foot-pounds. 

2.   Table  of  Materials  in  Electromotive  Order. 

(Electrochemical  Series.) 


DILUTE 
SULPHUEIC  ACID. 

DILUTE 
HYDROCHLORIC 
ACID. 

SOLUTION 
OF  SULPHIDE  OF 
POTASSIUM. 

SOLUTION  OF 
CAUSTIC  POTASH. 

1.  Zinc. 

1.  Zinc. 

1.  Zinc. 

1.  Zinc. 

2.  Cadmium. 

2.  Cadmium. 

2.  Copper. 

2.  Tin.               i 

3.  Tin. 

3.  Tin. 

3.  Cadmium. 

3.  Cadmium,     i 

4.  Lead. 

4.  Lead. 

4.  Tin. 

4.  Antimony. 

.H    5.  Iron. 

5.  Iron. 

5.  Silver. 

5.  Lead. 

J    6.  Nickel. 

6.  Copper. 

6.  Antimony. 

6.  Bismuth.     ^ 

5    7.  Bismuth. 

7.  Bismuth. 

7.  Lead. 

7.  Iron.             = 

— 

5    8.  Antimony. 

8.  Nickel. 

8.  Bismuth. 

8.  Copper.        5 

9.  Copper. 

9.  Silver. 

9.  Nickel. 

9.  Nickel. 

'    10.  Silver. 

10.  Antimony. 

10.  Iron. 

10.  Silver. 

I    11.  Gold. 

11.  ... 

11.  .  . 

11.  ... 

12.  Platinum. 

12.  ... 

12.  .  . 

12.  ... 

13.  Carbon. 

13.  ... 

13.  .  .  . 

13.  .  .  . 

591 


592  SCHOOL  PHYSICS. 

For  any  given  solution,  the  farther  apart  any  two  materials  are 
in  the  electromotive  table,  the  stronger  will  be  the  electrical  effect  of 
a  cell  with  plates  made  of  such  materials. 

3.  Table  of  Resistivities.  —  Represent  the  length  of  a  conducting 
wire  measured  in  feet  by  /,  its  diameter  measured  in  thousandths  of 
an  inch  (mils)  by  d,  and  its  resistance  measured  in  ohins  by  r.  In  the 
formula 


K  represents  a  constant  that  depends  upon  the  material  of  the  wire 
and,  for  the  substances  considered,  is  as  given  in  the  following  table 
of  resistivities:  — 


Silver 9.84 

Copper 10.45 

Zinc  .  .  36.69 


Mercury 58.24 

Platinum 59.02 

Iron  .  .  63.35 


German-silver  ....  128.29 

These  values  of  K  are  computed  for  the  temperature  of  20°.  Thus 
the  resistance  of  1,000  feet  of  No.  0000  copper  wire  at  20°,  is 
10.45  x  1,000  -4-  4602  =  0.049  +  ohms. 

4.  Dimensions  and  Functions  of  Copper  Wires.  —  In  the  table  given 
on  the  next  two  pages,  the  second  column  gives  the  diameters  in  mils, 
i.e.,  thousandths  of  an  inch ;  the  third  column  in  millimeters.  The 
fourth  column  gives  the  equivalent  number  of  wires  each  one  mil  in 
diameter.  By  multiplying  the  numbers  in  the  sixth  column  by  5.28, 
the  resistances  per  mile  may  be  found.  The  resistance  for  any  other 
metal  than  copper  may  be  found  by  multiplying  the  resistance  given 
in  the  table  by  the  ratio  between  the  resistivity  of  copper  and  that 
of  the  given  metal.  The  resistances  given  in  the  table  are  for  pure 
copper  wire.  Ordinary  commercial  copper  wire  has  a  lower  conduc- 
tivity than  that  of  pure  copper.  Consequently,  the  resistances  of 
such  wires  will  be  greater  than  those  given  in  the  table. 


APPENDIX. 


593 


Ml 

AXIOVdVQ 


i— i  ?b  CM  co  10  cc  i— i  ci  i^ 

CC   <M   ?1   l-l   T-I    r-l   ,-1 


TJH  -O  CC  Ol  Ol  i-l  1-1  1-1  ri 


CC  CC 
O  GO  GO 

o  o  o  d  »H 


CO  <3l  CO  K3  1Q  CO  r4  fc«»  «  IQ  CO  fc«>  b»  «H  00  OO 


CC  CJ  ^  ^-,  rt 


I 


O 

1 

I 

T3 

§ 
s 

.2 

*« 

S    ' 

I 

p 


•  — 


CC  <M  CM  1-1  1-1  i-l 


o<oooooc>ccooocoooocc> 


Si 

o 


ut  c  c        cc       o  c^        tc  c:  -f 

Ct-CtClt^CC^Oi^^^Ci 


8O  P  <5  O  O  O  O  Q  O  O  O  Q  O  <N  00  i-l  -^  GO  ^_     __ 
9  o  K3  o  eo  04  *-i  9  cj  co  S  eo  a  TP  o  «D  oo  QD  c*i^b  o 
o  QD  OD  o  eo  00  TH  eo  Cb  o  09  •<«  ^r  OD  t^~ao  c%  o  O  ao  ci  eo 

§Oi  "^t4  ^*  O^  t^*  OS  "^f^  i—H  Ol  ^^  GO  ^^  *"H  <O  O^  T-^  ^^  t^»  ^^  lO  !O 
OOCsJCOOOlOCOCO-^OJr-tOO5GOl>.CDlOlC-^tTtl 


38 


594 


SCHOOL   PHYSICS. 


"*OOO<MlOt>-iOi— Ib- 
GOl^COiO^OtKMfMCM— I 


T-Hi— IrH 


I 

I 
a 


M  GO 


<<*OOOfc»CO^*»O<»b- 

CM  a:  T— lOacooaooGOcofM'— ( 


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T-HO51>.COThCOCO<Mr- I  i— I  i— I 


I—  UO  Ol  rH  i-l  r-l  O  10  O  O  O  O  O  O 
iOCOfMQOrH 


r-lrHi— ICN(MCOTtHiOOc6ocO«Oi— l«OCOQICOt>.CM 

»  TH   TH 


a 

H 

1^05 


20 

H 


fMOi—  iT^i—  ( 


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o  o  o  o  o 


-T- 

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rHiOiOi— It— lCD»Ot>-(MOOCOl>-CO»— I  O 
THiOOO<NGOlQ<NOOOQD^TQl»MOQ& 


GOt^?DlOlOT^^COCO(M(MCM(MT-H^HTH^-lr-lrHOO 


QJ  (^  ?O  TtH  1>-  O 
COOST^CO  kOrH 

CO  CO  CM  (M  (M  CM 


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r-<CM<MCM(MCMCM<MCMCM(MCOCOCOCOCOCOCOCOCOCOr^ 


APPENDIX. 


595 


5.   Table  of  Natural  Tangents. 


ARC. 

TAXGEXT. 

ARC. 

TAXGEXT. 

ARC. 

TAXGEXT. 

ARC. 

TAXGEXT. 

0° 

.000 

23° 

.424 

46° 

1.036 

69° 

2.61 

1 

.017 

24 

.445 

47 

1.07 

70 

2.75 

2 

.035 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.15 

72 

3.08 

•4 

.070 

27 

.510 

50 

1.19 

73 

3.27 

5 

.087 

28 

.532 

51 

1.23 

74 

3.49 

6 

.105 

29 

.554 

52 

1.28 

-  75 

3.73 

7 

.123 

30 

.577 

53 

1.33 

76 

4.01 

8 

.141 

31 

.601 

54 

1.38 

77 

4.33 

9 

.158 

32 

.625 

55 

1.43 

78 

4.70 

10 

.176 

33 

.649 

56 

1.48 

79 

5.14 

11 

.194 

34 

.675 

57 

1.54 

80 

5.67 

12 

.213 

35 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

59 

1.66 

82 

7.12 

14 

.249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

62 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.05 

87 

19.08 

19 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.933 

66" 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Infinite. 

22 

.404 

45 

1.000 

68 

2.48 

596 


SCHOOL  PHYSICS. 


6.    Table  of  Natural  Sines. 


ARC. 

SINE. 

ARC. 

SINE. 

ARC. 

SINE. 

ARC. 

SINE. 

0° 

0.000 

23 

0.391 

46° 

0.719 

69° 

0.934 

1 

0.017 

24 

0.407 

47 

0.731 

70 

0.940 

2 

0.035 

25 

0.423 

48 

0.743 

71 

0.946 

3 

0.052 

26 

0.438 

49 

0.755 

72 

0.951 

4 

0.070 

27 

0.454 

50 

0.766 

73 

0.956 

,  5 

0.087 

28 

0.469 

51 

0.777 

74 

0.961 

'  6 

0.105  - 

20 

0.485 

52 

0.788 

75 

0.966 

7 

0.122 

30 

0.500 

53 

0.799 

76 

0.970 

8 

0.139 

31 

0.515 

54 

0.809 

77 

0.974 

9 

0.156 

32 

0.530 

55 

0.819 

78 

0.978 

10 

0.174 

33 

0.545 

56 

0.829 

79 

0.982 

11 

0.191 

34 

0.559 

57 

0.839 

80 

0.985 

12 

0.208 

35 

0.574 

58 

0.848 

81 

0.988 

13 

0.225 

36 

0.588 

59 

0.857 

82 

0.990 

14 

0.242 

37 

0.602 

60 

0.866 

83 

0.993 

15 

0.259 

38 

0.616 

61 

0.875 

84 

0.995 

16 

0.276 

39 

0.629 

62 

0.883 

85 

0.996 

17 

0.292 

40 

0.643 

63 

0.891 

86 

0.998 

18 

0.309 

41 

0.656 

64 

0.899 

87 

0.999 

19 

0.326 

42 

0.669 

65 

0.906 

88 

0.999 

20 

0.342 

43 

0.682 

66 

0.914 

89 

0.999 

21 

0.358 

44 

0.695 

67 

0.921 

90 

1.000 

22 

0.375 

45 

0.707 

68 

0.927 

INDEX. 


NUMBERS  REFER  TO  PAGES  UNLESS  OTHERWISE  INDICATED. 


Aberration,  Chromatic,  371. 

Spherical,  339,  363. 
Abscissas,  Axis  of,  95. 
Absolute  temperature,  274. 

unit  of  force,  67. 

zero,  273. 
Absorption  of  gases,  50. 

of  radiation,  386. 
Acceleration,  58. 

due  to  gravity,  110,  123. 
Accordion,  261. 
Accumulator,  Electric,  561. 
Achromatic  lens,  371. 
Acoustics,  201. 
Activity,  85. 
Adhesion,  29. 
Aeriform  body,  39. 
^Esculin,  see  esculin. 
Agonic  lines,  476. 
Air,  182. 

Air  columns,  Vibratory,  260. 
Air  pump,  194. 
Air  thermometer,  272. 
Alternating  currents,  502,  515. 
Alternator,  500. 
Amalgamating  zinc,  433. 
Ammeter,  527,  543. 
Ampere,  445,  523,  524. 


Ampere's  theory  of  magnetism,  473. 
Ampere-turns,  469. 
Amplitude  of  oscillation,  119. 

of  vibration,  208. 
Analysis  of  light,  368. 

Spectrum,  381. 
Analyzer,  399. 
Aneroid  barometer,  185. 
Angle  of  polarization,  398. 
Anion,  559. 
Annealing,  30. 
Anode,  559. 
Anti-nodes,  236. 
Aperture  of  mirror,  333. 
Aqueous  humor,  402. 
Archimedes,  162. 
Arc  lamps,  548. 

lighting,  547. 
Armature  of  dynamo,  490. 

of  magnet,  456. 
Astatic  galvanometer,  525. 

needle,  458. 
Athermancy,  385. 
Atmospheric  electricity,  516. 

pressure,  182. 
Atom,  10. 
Atomic  forces,  15. 
Atwood  machine,  109,  117. 
Axis  of  lens,  357. 

of  mirror,  333. 


597 


598 


SCHOOL  PHYSICS. 


Nwmbers  refer  to  Pages  unless  otherwise  indicated. 


Balance,  133. 

Ballistic  galvanometer,  527. 

Barometer,  184. 

Base,  101. 

Battery,  Electric,  429. 

Voltaic,  438,  481,  482. 
Beam  of  rays,  313. 
Beams,  Rigidity  of,  36. 
Beats,  Acoustic,  252. 
Bells,  Electric,  555. 

Vibrations  of,  265. 
Bell  telephone,  570. 
Blake  transmitter,  572. 
Blind  spot,  403. 
Block  and  tackle,  142. 
Body,  9. 

Boiling-point,  272,  291. 
Bolometer,  575. 

"Bound"  electric  charges,  427. 
Boyle's  law,  189. 
Breaking  strength,  35,  37. 
Bright-line  spectra,  382. 
Brush  arc  lamp,  549. 

dynamo,  495. 
Bunsen  cell,  480. 

photometer,  323. 
Burning  glass,  347. 

C. 

Calipers,  34. 
Calorescence,  389. 
Calorimetry,  299. 
Calory,  300,  447. 
Candle,  Standard,  323. 
Capacity,  Electrical,  426,  534. 

Thermal,  303. 
Capillary  attraction,  47. 

tubes,  48.- 
Capstan,  140. 


Carhart-Clark  cell,  443. 

Cathode,  559. 

Cation,  559. 

Celsius  thermometer,  273. 

Center  of  mass,  99,  100. 

Centigrade  thermometer,  273. 

Centrifugal  force,  78. 

C.G.S.  units,  68. 

Charge,  Electric,  415,  419. 

Residual,  429. 
Chemical  changes,  12. 

effects  of  electric  current,  557 

effects  of  radiation,  387. 
Chemism,  15. 
Chladni's  plates,  265. 
Chords,  Musical,  232. 
Choroid  coat,  401. 
Chromatic  aberration,  371. 

scale,  233. 
Chromatics,  368. 
Chromic  acid  cell,  480. 
Circuit,  Electric,  437. 
Clarinet,  261. 
Clocks,  123,  126. 
Clouds,  516. 
Coefficient  of  elasticity,  29. 

of  expansion,  285,  299. 

of  friction,  130,  137,  138. 

of  self-induction,  504. 
Coercive  force,  471. 
Cohesion,  29. 
Coincident  waves,  245. 
Colloids,  53. 
Color,  372. 
Color  blindness,  403. 
Commutator,  492,  507,  539. 
Complementary  colors,  374. 
Condensation,  290. 
Condenser,  Electric,  427,  507. 
Condensing  pump,  196. 
Conduction,  Electric,  414,  416. 


IXDEX. 


599 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Conduction,  Thermal,  278,  279. 
Conductivity,  Electric,  441. 
Conjugate  foci,  220,  335,  359. 
Convection,  278,  282. 

Electric,  420. 
Co-ordinates,  Axes  of,  95. 
Cork-screw  rule,  468. 
Cornea,  401. 
Coulomb,  445,  523,  524. 
Coulomb's  torsion  balance,  523. 
Couple,  71. 
Co-vibration,  244. 
Critical  angle,  353. 
Crova  disk,  216. 
Crown  of  cups,  519. 
Crystalline  lens,  401. 
Crystallization,  41. 
Crystalloids,  53. 

Current  electricity,  422,  433,  437. 
Curvilinear  motion,  77. 

D. 

Daniell  cell,  443,  480,  538. 
Dark-line  spectra,  382. 
Dead-beat  galvanometer,  527. 
Declination,  Magnetic,  475. 
Density  of  matter,  167. 

Electric,  419. 
Deprez    d'Arsonval    galvanometer, 

527. 

Deviation  of  rays,  356. 
Dew-point,  290,  299. 
Dialysis,  53. 
Diamagnetic,  456. 
Diathermancy,  385. 
Diatonic  scale,  232. 
Dielectric,  415,  430. 

constant,  426. 
Differential  galvanometer,  527. 

thermometer,  272. 


Diffraction,  394. 

grating,  396. 
Diffusion  of  gases,  52. 

of  heat,  278. 

of  radiant  energy,  328.  , 

Dip,  Magnetic,  475. 
Dipping  needle,  458. 
Discharge,  Electric,  513. 
Discharger,  429. 
Disgregation,  300. 
Dispersion,  Irrationality  of,  396. 

of  light,  368. 

Distance,  Estimation  of,  403. 
Distillation,  293. 
Divisions  of  matter,  10. 
Double  refraction,  397,  399. 
Ductility,  32. 
Duplex  telegraph,  565. 
Dynamo,  489. 
Dynamometer,  68. 
Dyne,  67. 

E. 

Ebullition,  290,  292. 
Echoes,  220. 

Edison  3- wire  system,  544. 
Efficiency  of  machines,  129. 
Elastic  force  of  gases,  186. 
Elasticity,  28. 

and  reaction,  76. 
Electric  accumulator,  561. 

action,  Laws  of,  418. 

arc,  547. 

battery,  429. 

bells,  555. 

capacity,  426. 

circuit,  437. 

condenser,  427. 

current,  422,  433,  437,  465,  486. 

density,  419. 


600 


SCHOOL  PHYSICS. 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Electric  discharge,  513. 

field,  421. 

fire  alarm,  556. 

gas  lighting,  552. 
?  generators,  478. 

induction,  425. 

lighting,  543,  547. 

lines  of  force,  421. 

machines,  509. 

measurements,  523. 

motors,  553. 

oscillations,  580. 

pendulum,  413. 

resonance,  583. 

units,  418,  426. 

waves,  581. 

welding,  552. 
Electricity,  412. 

Atmospheric,  516. 

Nature  of,  429. 
Electrification,  414,  416,  420,   423, 

431. 

Electrochemical  series,  591. 
Electrodes,  437. 
Electrodynamics,  453. 
Electrodynamometer,  528. 
Electrolysis,  557. 
Electrolyte,  559. 
Electromagnet,  472. 
Electromagnetic  induction,  484. 

radiation,  579. 

telegraph,  564. 

theory  of  light,  588. 

units,  418,  524. 

waves,  581. 

Electrometallurgy,  559. 
Electrometer,  523. 
Electromotive  force,  424,  443,  534, 
577. 

table,  591. 
Electrophorus,  509. 


Electroplating,  560. 
Electroscope,  417. 

Condensing,  519. 
Electrostatic  units,  418,  623. 
Electrotyping,  560. 
Element,  12. 
Endosmosis,  53. 
Energy,  12,  85. 

Conservation  of,  90. 

Measurement  of,  88,  89,  90. 

Kadiant,  312. 

Relation  to  velocity,  88. 

Types  of,  86. 

Units  of,  88,  89. 
Engine,  Steam,  308. 
Equilibrant,  69. 
Equilibrium,  101. 
Equipotential  surfaces,  422. 
Erg,  84. 
Esculin,  388. 
Ether,  312,  429. 
Evaporation,  289,  290. 
Exosmosis,  53. 
Expansion,  27,  271,  283,  297. 
Experiment,  16. 
Extension,  16. 

Measurement  of,  17. 
Eye,  the  human,  401. 

F. 

Fahrenheit  hydrometer,  170. 

thermometer,  273. 
Falling  bodies,  106,  111. 
Farad,  426,  523,  524. 
Far-sight,  402. 
Field,  Electric,  421. 

magnet,  494. 

Magnetic,  458. 

of  force,  421. 
Fife,  261. 
Films,  Superficial,  44. 


INDEX. 


601 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Fire  alarm,  Electric,  556. 
Flats  and  sharps,  234. 
Flotation,  165. 
Fluid,  38. 
Fluorescence,  388. 
Flute,  261. 

Flux  of  force,  461,  535. 
Focal  length,  335,  365. 
Focus,  333,  334,  358,  360. 
Foot-pound,  84. 
Foot-poundal,  84. 
Force,  15. 

Centrifugal,  78. 

Coercive,  471. 

Composition  of,  70,  73,  81,  82. 

Electromotive,  424. 

Elements  of,  66. 

Flux  of,  461,  535. 

Graphic  representation  of,  69. 

Magnetomotive,  468,  536. 

Measurement  of,  67. 

Moment  of,  132. 

Parallelogram  of,  71. 

pump,  194. 

Kesolution  of,  74. 

Units  of,  67. 
Foucault  currents,  491. 
F.P.S.  units,  68. 
Fraunhofer  lines,  383. 
Freezing-point,  272. 
Friction,  129,  137,  138. 
Frictional  electric  machine,  509. 

electricity,  412. 
Fundamental  tones,  236. 
Fusing-point  pressure,  293. 
Fusion,  288. 

Latent  heat  of,  300. 

G. 

Galilean  telescope,  408. 
Galileo,  109. 


Galvanometer,  525. 
Galvanoscope,  439,  484. 
Gamut,  230. 
Gas,  39. 

lighting,  Electric,  552. 
Gases,  Kinetic  theory  of,  52. 

Mechanics  of,  179. 
Gauss,  461,  476. 
Geissler  tube,  519,  520. 
Gilbert,  469. 
Glass  working,  21. 
Graduate,  20. 
Gram,  22. 

Graphic  study  of  sound,  238. 
Gravitation,  95. 

Law  of,  96. 
Gravity,  96. 

cell,  480. 

Center  of,  99. 

unit  of  force,  67. 
Grenet  cell,  479. 
Grove  cell,  480. 

H. 

Halo,  395. 
Hanchett  cell,  435. 
Hardness,  30. 
Harmonic  motion,  208. 
Harmonics,  236. 
Hearing,  230. 
Heat,  12,  270. 

Diffusion  of,  278. 

Latent,  300. 

Mechanical  equivalent  of,  307. 

Production  of,  277. 

Sensible,  300. 

units,  299. 
Henry,  The,  504. 
Hertz  experiments,  584. 
Homogeneous  light,  372. 
Horse-power,  85. 


602 


SCHOOL  PHYSICS. 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Humidity,  291. 
Hyaloid  membrane,  402. 
Hydraulic  press,  153. 
Hydrometer,  168. 
Hygrometer,  291. 
Hypermetropia,  402. 
Hypothesis,  13. 
Hypsometer,  293. 


Iceland  spar,  397. 
Identity,  Electrical,  513. 
Image,  318,  332,  336,  361. 
Impedance,  504,  505,  586. 
Impenetrability.  21. 
Incandescence  lighting,  543. 
Inclination,  Magnetic,  475. 
Inclined  plane,  143. 
Indestructibility,  25. 
Index  of  refraction,  350. 
Induced  electric  currents,  486,  488. 
Induction  coil,  506. 

Electric,  425. 

Electromagnetic,  484. 

Self,  503. 

Inductive  capacity,  426. 
Inertia,  26. 

Center  of,  99. 
Insulators,  414. 
Intensity  of  sound,  225,  226. 
Interference  of  radiation,  393. 
'    of  sound,  251,  257. 
Intermolecular  spaces,  11. 
Interrupter,  502. 
Intervals,  Musical,  230. 
Ions,  559. 
Iris,  402. 
Irradiation,  396. 
Irrationality  of  dispersion,  396. 
Isoclinic  lines,  475. 


Isodynamic  lines,  475. 
Isogonic  lines,  475. 

J. 

Jolly  balance,  178. 
Joule,  446,  523. 
Joule's  law,  447. 
Joule's  principle,  307. 


Kathode,  see  Cathode. 
Ration,  see  Cation. 
Key-note,  230. 
Key,  Telegraph,  565. 
Kicking  coil,  552. 
Kilogram,  22. 
Kilogram  meter,  84. 
Kinetic  energy,  86. 

theory  of  gases,  52. 
Kinnersley  thermometer,  523. 


L. 

Law,  14. 

Leclanchc*  cell,  443,  480. 

Lens,  371. 

Lever,  130. 

Ley  den  jar,  428. 

Lift  pump,  193. 

Light,  314. 

Electromagnetic  theory  of,  588. 

Intensity  of,  321. 

Velocity  of,  320. 
Lightning,  516. 

rod,  574. 

Lines  of  force,  421,  460. 
Liquefaction,  287. 
Liquid,  39. 
Liquids,  mechanics  of,  150. 


INDEX. 


603 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Liter,  19. 

Local  action,  479. 
currents,  491. 
Lodestone,  456. 
Longitudinal  waves,  211. 
Loudness  of  sound,  225,  226. 


M. 

Mach  apparatus,  212. 
Machines,  127. 

Efficiency  of,  129. 

Laws  of,  128. 

Magdeburg  hemispheres,  181. 
Magic  lantern,  410. 
Magnet,  455. 

Field,  494. 
Magnetic  field,  458,  535. 

lines  of  force,  460. 

mass,  461. 

needles,  457. 

p*hantom,  459,  478. 

potential,  463. 

resistance,  470. 

substances,  456. 

transparency,  462. 
Magnetism,  454,  473. 

Residual,  473. 
Magnetite,  456., 

Magnetization,  456,  463,  465,  536. 
Magneto,  488. 

Magnetomotive  force,  468,  536. 
Magnetoscope,  481. 
Magnifying  glass,  406. 

power,  367,  406,  409. 
Malleability,  32. 
Manometric  flames,  239. 
Mariotte's  law,  190. 
Mass,  11,  12. 

Center  of,  99,  100. 

Measurement  of,  22. 


Matter,  9,  15. 

Conditions  of,  38. 

Divisions  of,  10. 

Properties  of,  16. 

Radiant,  40. 

Structure  of,  9. 
Measurements,  Delicacy  of,  24. 

Electrical,  523. 

Mechanical  equivalent  of  heat,  307. 
Mechanics,  57. 
Medium  of  radiation,  312,  429. 

of  sound,  206. 
Megohm,  440. 
Melodeon,  261. 
Meter,  17. 

Metric  measures,  18,  19,  23. 
Mho,  441. 
Microfarad,  426. 
Microhm,  440. 
Microphone,  569. 
Microscope,  406. 
Milliampere,  445. 
Mirror,  Concave,  333,  346. 

Convex,  340,  346. 

galvanometer,  526. 

galvauoscope,  484,  498. 

Plane,  331,  342. 
Molar  forces,  15. 

motion,  12. 
Molecular  attraction,  29. 

forces,  15. 

motion,  12. 
Molecules,  11. 

Superficial,  43. 
Moment  of  force,  132. 
Momentum,  62. 
Monochromatic  light,  372. 
Morse  alphabet,  564. 
Motion,  57. 

Accelerated,  Laws  of,  60. 

Composition  of,  61. 


604 


SCHOOL  PHYSICS. 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Motion,  Curvilinear,  77. 

Forms  of,  12,  206,  207,  208. 

Graphic  representation  of,  60. 

Laws  of,  65,  74. 

Parallelogram  of,  61. 

Reflected,  76,  77. 

Resolution  of,  62. 

Resultant,  69. 
Motors,  Electric,  563. 
Multiple  arc,  438,  481. 
Multiplex  telegraph,  566. 
Music  and  noise,  253. 
Musical  intervals,  230. 

scale,  230. 
Myopia,  402. 


N. 

Near-sight,  402. 
Needle,  Magnetic,  457. 
Newton's  disk,  370. 

laws  of  motion,  65. 

rings,  393. 

Nicholson  hydrometer,  168. 
Nicol  prism,  399. 
Nodes,  234. 
Noise  and  music,  253. 
Normal  spectrum,  396. 


O. 

Obscure  heat,  385. 
Octave,  230,  231. 
Oersted,  470. 
Ohm,  440,  523,  524. 
Ohm's  law,  446. 

law,  Analogue  of,  470. 
Old-sight,  402. 
Opacity,  316. 
Opera  glass,  408. 
Optical  angle,  403. 


Optical  center,  357. 

lantern,  409. 

study  of  sound,  241. 
Ordinates,  Axis  of,  95. 
Organ-pipe,  261. 
Oscillation,  Center  of,  122. 

of  pendulum,  119. 
Oscillations,  Electric,  580. 
Oscillator,  Tesla's,  501. 
Oscillatory  electric  discharge,  514. 
Osmose,  53. 
Overtones,  234. 

P. 

Parallel  grouping  of  voltaic  cells, 

438,  481. 

Paramagnetic,  456. 
Partial  tones,  236. 
Pascal,  152,  184. 
Pencil  of  rays,  313. 
Pendular  motion,  207. 
Pendulum,  118. 

Electric,  413. 

Torsional,  28. 
Penumbra,  318. 
Period  of  oscillation,  119. 

of  vibration,  208,  210. 
Permeability,  469,  536. 
Persistence  of  vision,  403. 
Phantom  curves,  459,  478. 
Phenomenon,  13. 
Phosphorescence,  388. 
Photographer's  camera,  405. 
Photometry,  322. 
Physical  changes,  13. 
Physics,  16. 
Piano  scale,  234. 
Pigments,  Mixing,  377. 
Pipe  instruments,  261. 
Pitch  of  sounds,  225,  228,  231. 


INDEX. 


605 


Numbers  refer  to  Pages 

Plater,  560. 

Plates,  Vibrations  of,  264. 

of  voltaic  cell,  437. 
Pliicker  tube,  392. 
Pneumatics,  179. 
Polariscope,  399. 
Polarization  of  cell,  435,  479. 

of  light,  397,  579. 
Polarizer,  399. 
Poles,  Magnetic,  456,  462. 

of  voltaic  cell,  437. 
Porosity,  27. 

Potassium  dichromate  cell,  479. 
Potential,  Electric,  422,  444,  534. 

energy,  86. 

Magnetic,  463. 
Poundal,  67. 
Power,  128. 
Presbyopia,  402. 
Pressure,  Fluid,  151,  182. 

-gauge,  160. 
Prevost's    theory    of     exchanges, 

385. 

Primary  battery,  561. 
Prism,  355. 

Prismatic  spectrum,  369. 
Projectiles,  112. 
Proof-plane,  417. 
Properties  of  matter,  16. 
Pulley,  141,  149. 
Pumps,  193. 
Pupil  of  eye,  402. 

Q 

Quadruplex  telegraph,  566. 
Qualitative  experiment,  16. 
Quality  of  sound,  225,  236. 
Quantitative  experiment,  16. 
Quantity,  Electric,  418. 


unless  otherwise  indicated. 
R. 

Radiant  energy,  312,  385,  387. 

heat,  385. 

matter,  40. 
Radiation,  312. 

Intensity  of,  321. 
Rainbow,  377. 
Range  of  projectile,  113. 
Rarefaction,  Waves  of,  210. 
Ray,  313. 
Reactance,  504. 
Reaction,  66,  74,  75,  76. 
Reaumur  thermometer,  273. 
Reed  instruments,  261. 
Reflection  of  electrical  waves,  585. 

of  motion,  76,  77. 

of  radiation,  326. 

of  sound,  219. 

Total,  351. 
Refraction  of  electrical  waves,  685. 

Double,  397,  399. 

Index  of,  350. 

of  radiation,  346. 

of  sound,  221. 
Refractor,  407. 
Regelation,  295.^ 
Register,  Telegraph,  565. 
Relay,  Telegraph,  567. 
Reluctance,  470. 
Reluctivity,  470. 
Remanance,  471. 
Repeater,  Telegraph,  569. 
Residual  charge,  429. 

magnetism,  473. 
Resistance  coils,  529. 

Electric,  439,  441,  442,  447,  480, 
531,  533. 

Magnetic,  470. 
Resistivity,  441,  592. 
Resonance,  Acoustic,  249,  254. 


606 


SCHOOL  PHYSICS. 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Resonance,  Electric,  583. 
Resultant,  69. 
motion,  69. 
Retina,  401. 
Rheocord,  538. 
Rhumkorff  coil,  506. 
Rigidity  of  beams,  36. 
Rods,  Vibrations  of,  263. 
Rumford  photometer,  322,  325. 

S. 

Scales,  Musical,  230,  232,  233. 

Science,  9. 

Sclerotic  coat,  401. 

Screw,  147. 

Secondary  cells,  560. 

Self-induction,  503. 

Series  grouping  of  voltaic  cells,  438, 

482. 

Shadows,  316. 
Sharps  and  flats,  234. 
Shunt,  448. 

Sine  galvanometer,  526. 
Sines,  Natural,  596. 
Sinusoidal  curve,  209,  211. 
Siphon,  190,  199. 
Siren,  228. 

Size,  Estimation  of,  403. 
Sky,  The  color  of,  374. 
Smee  cell,  479. 
Soap  bubbles,  56. 
Sodium  dichromate  cell,  479. 
Solar  spectrum,  369. 
Solenoid,  467. 
Solid,  38. 
Solidification,  288. 
Solution,  40,  287. 
Sonometer,  235,  246,  258. 
Sound,  201. 

Cause  of,  202. 


Sound,  Characteristics  of,  225. 

media,  206. 

Reflection  of,  219. 

Refraction  of,  221. 

Velocity  of,  218,  223. 

waves,  209,  210. 
Sounder,  Telegraph,  566. 
Sound-mill,  247. 
Specific  gravity,  167. 

gravity  bulb,  170. 

gravity  flask,  170. 

heat,  302.    ,  . 

inductive  capacity,  426. 

magnetic  resistance,  470. 

resistance,  441. 
Spectroscope,  379. 
Spectrum,   368,  369,  372,  379,  382, 
383,  396. 

analysis,  381. 
Speculum,  408. 
Spherical  aberration,  363. 
Spheroidal  state,  293. 
Spy-glass,  407. 

Square  root  of  mean  square,  505. 
Stability,  102. 
Static  electricity,  412,  512. 
Steam-engine,  308. 
Stereopticon,  410. 
Stereoscope,  404. 
Still,  294. 

Storage  battery,  561. 
Strain,  27. 
Stress,  27. 

Stretching  weight,  37. 
Structure  of  matter,  9,  10. 
Sublimation,  293. 
Substance,  9. 
Sucker,  196. 
Sucking  magnet,  551. 
Suction  pump,  93. 
Surface  density,  419. 


OF 


Numbers  refer  to  Page*  unless  otherwise  indicated. 


Surface  tension,  45. 

viscosity,  44. 

Sympathetic  vibrations,  245,  247. 
Synthesis  of  light,  369. 

T. 

Tangent  galvanometer,  525. 
Tangents,  Natural,  595. 
Telegraph,  562. 
Telephone,  487,  570. 
Telescope,  407. 
Temperament,  234. 
Temperature,  270. 

Absolute,  274. 

Absolute  zero  of,  273. 
Tempering,  30. 
Tenacity,  31. 

Terrestrial  magnetism,  474. 
Tesla,  Nikola,  388,  501,  585. 
Theory,  13. 
Therm,  300. 
Thermal  effects  of  radiation,  385. 

unit,  299. 

Thermo-dynamics,  306. 
Thermo-electricity,  518. 
Thermometer,  271,  275,  523.     „ 
Thermoscope,  271,  518. 
Thunder,  517. 
Timbre,  225,  236. 
Torpedo,  454. 
Torricelli,  183. 
Torsion,  37. 

balance,  523. 

pendulum,  28. 
Total  reflection,  352. 
Touch  paper,  204. 
Tourmaline  tongs,  397. 
Transformer,  505,  546. 
Transparency,  Optical,  316. 

Magnetic,  462. 


Turbine  wheel,  172. 


U. 

Umbra,  318. 

Units,  Electric,  418,  426,  523. 

Metric,  18,  19,  23. 

Thermal,  299. 


V. 

Vapor,  39. 
Vaporization,  289. 

Latent  heat  of,  302. 
Variation,  Magnetic,  475. 
Velocity,  57. 

Relation  to  energy,  88 

of  sound,  218,  223. 
Vibgyor,  369. 
Vibration,  Laws  of,  258. 
Vibratory  motion,  206. 
Vibroscope,  238. 
Visual  angle,  403. 
Vitreous  humor,  402. 
Volt,  443,  523,  524. 
Voltaic  arc,  547. 

battery,  438,  481,  482. 

cell,  437,  443,  478. 
Voltameter,  560. 
Voltmeter,  528. 
Vortex-ring,  473. 


W. 

Water  power,  171. 

wheels,  172. 
Watt,  85,  446,  447,  523. 
Wattmeter,  529. 
Wave  forms,  208. 

length,  210,  211. 

motion,  206,  209,  210. 


608 


SCHOOL  PHYSICS. 


Numbers  refer  to  Pages  unless  otherwise  indicated. 


Weber,  461,  476. 
Wedge,  146. 
Weighing,  133. 
Weight,  21,  97,  128. 

Law  of,  97. 

Measurement  of,  22. 
Welding,  Electric,  552. 
Wheatstone  bridge,  532,  535,  541. 
Wheel  and  axle,  139. 
Whirling  table,  78. 
Whistle,  261. 

Wimshurst  electric  machine,  510. 
Windlass,  140. 
Wire,  Breaking  strength  of,  35. 


Wire  gauge,  34. 

Table  of  dimensions,  etc.,  592. 
Wiring  for  electric  lights,  544. 
Work,  83. 

units,  84. 


Y. 

Yard,  17. 
Yellow  spot,  403. 


Zinc,  Amalgamation  of,  433. 


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